{"id":425,"date":"2022-04-13T10:57:37","date_gmt":"2022-04-13T10:57:37","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=425"},"modified":"2025-04-08T12:16:36","modified_gmt":"2025-04-08T12:16:36","slug":"w-3-truth-tables","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/w-3-truth-tables\/","title":{"rendered":"W.3 Truth tables"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"> <strong>Truth tables<\/strong><\/h2>\n\n\n\n<p class=\"has-text-align-left has-text-color has-link-color has-huge-font-size wp-elements-b2e7650aa86b148359a91f7caeb21bbd\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-137efc08e4cdec9a1994f731f61821d3\" style=\"color:#000060\"><strong>What is a Truth Table?<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A <strong>truth table<\/strong> is a chart used to show <strong>all possible truth values<\/strong> of a logical expression.<\/li>\n\n\n\n<li>It helps in understanding how <strong>logical operators<\/strong> (AND, OR, NOT) affect the result.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-03469111c58beb747792dc80b7c1322c\" style=\"color:#000060\"><strong>Basic Logic Values<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>True (T)<\/strong> = 1<\/li>\n\n\n\n<li><strong>False (F)<\/strong> = 0<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-ca9229f51fec187fef0972d69cb64d89\" style=\"color:#000060\"><strong>Common Logical Operators<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Operator<\/th><th>Symbol<\/th><th>Meaning<\/th><\/tr><\/thead><tbody><tr><td>NOT<\/td><td>\u00ac or ~<\/td><td>Reverses the truth value<\/td><\/tr><tr><td>AND<\/td><td>\u2227<\/td><td>True only if both values are true<\/td><\/tr><tr><td>OR<\/td><td>\u2228<\/td><td>True if at least one is true<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-f56f164dbcfad9d54b6ece6f168511b9\" style=\"color:#000060\"><strong>Truth Tables for Basic Operations<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>A. NOT (\u00acA)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>A<\/th><th>\u00acA<\/th><\/tr><\/thead><tbody><tr><td>T<\/td><td>F<\/td><\/tr><tr><td>F<\/td><td>T<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-large-font-size\"><strong>B. AND (A \u2227 B)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>A<\/th><th>B<\/th><th>A \u2227 B<\/th><\/tr><\/thead><tbody><tr><td>T<\/td><td>T<\/td><td>T<\/td><\/tr><tr><td>T<\/td><td>F<\/td><td>F<\/td><\/tr><tr><td>F<\/td><td>T<\/td><td>F<\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-large-font-size\"><strong>C. OR (A \u2228 B)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>A<\/th><th>B<\/th><th>A \u2228 B<\/th><\/tr><\/thead><tbody><tr><td>T<\/td><td>T<\/td><td>T<\/td><\/tr><tr><td>T<\/td><td>F<\/td><td>T<\/td><\/tr><tr><td>F<\/td><td>T<\/td><td>T<\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-e75eabd2d6ad3e762325ef37eb303698\" style=\"color:#000060\"><strong>Constructing a Truth Table<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Step 1: List all possible combinations of truth values for variables (A, B, etc.)<\/li>\n\n\n\n<li>Step 2: Apply logical operators step by step.<\/li>\n\n\n\n<li>Step 3: Show the final result for each row.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-1d0e40a847f2839687c0ae9366fe693d\" style=\"color:#000060\"><strong>Why Are Truth Tables Important?<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>They help <strong>visualize<\/strong> and <strong>verify<\/strong> logical expressions.<\/li>\n\n\n\n<li>Useful in <strong>math<\/strong>, <strong>computer science<\/strong>, and <strong>digital circuits<\/strong>.<\/li>\n\n\n\n<li>Helps determine if a statement is always true (tautology), always false (contradiction), or sometimes true (contingency).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-a2ffa6b27fd8afdce107af58fe24706b\" style=\"color:#000060\"><strong>Example: (A \u2228 B) \u2227 \u00acA<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>A<\/th><th>B<\/th><th>A \u2228 B<\/th><th>\u00acA<\/th><th class=\"has-text-align-center\" data-align=\"center\">(A \u2228 B) \u2227 \u00acA<\/th><\/tr><\/thead><tbody><tr><td>T<\/td><td>T<\/td><td>T<\/td><td>F<\/td><td class=\"has-text-align-center\" data-align=\"center\">F<\/td><\/tr><tr><td>T<\/td><td>F<\/td><td>T<\/td><td>F<\/td><td class=\"has-text-align-center\" data-align=\"center\">F<\/td><\/tr><tr><td>F<\/td><td>T<\/td><td>T<\/td><td>T<\/td><td class=\"has-text-align-center\" data-align=\"center\">T<\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><td>T<\/td><td class=\"has-text-align-center\" data-align=\"center\">F<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#e9f4e9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-411a7f23b67d2e5b0bf0412363542435\" style=\"color:#b00012\"><strong>\ud83c\udf88 Complete&nbsp;the truth&nbsp;table.<\/strong><\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047268763_296\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>p\u2228q<\/td><\/tr><tr><td>T<\/td><td>T<\/td><td><\/td><\/tr><tr><td>T<\/td><td>F<\/td><td><\/td><\/tr><tr><td>F<\/td><td>T<\/td><td><\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fill&nbsp;in the third column. Determine if the value of either&nbsp;p&nbsp;or&nbsp;q&nbsp;is&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047268763_448\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>p\u2228q<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><tr><td><strong>F<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#dbcce8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-322965191926960912908ffdac9357d5\" style=\"color:#b00012\"> \ud83c\udf88<strong> Complete&nbsp;the truth&nbsp;table.<\/strong><\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047458359_415\" class=\"wp-block-table\"><table><tbody><tr><td>q<\/td><td>r<\/td><td>r\u2227q<\/td><\/tr><tr><td>T<\/td><td>T<\/td><td><\/td><\/tr><tr><td>T<\/td><td>F<\/td><td>F<\/td><\/tr><tr><td>F<\/td><td>T<\/td><td><\/td><\/tr><tr><td>F<\/td><td>F<\/td><td><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">&#8216;<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fill&nbsp;in the third column. Determine if the values of both&nbsp;r&nbsp;and&nbsp;q&nbsp;are&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047458359_590\" class=\"wp-block-table\"><table><tbody><tr><td>q<\/td><td>r<\/td><td>r\u2227q<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><tr><td>T<\/td><td>F<\/td><td>F<\/td><\/tr><tr><td><strong>F<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><tr><td><strong>F<\/strong><\/td><td><strong>F<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f6dacf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-484547f7652f06a3995c83c0b8e8aad8\" style=\"color:#b00012\">\ud83c\udf88<strong>Complete&nbsp;the truth&nbsp;table<\/strong>.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047578900_441\" class=\"wp-block-table\"><table><tbody><tr><td>q<\/td><td>r<\/td><td>r\u2227q<\/td><\/tr><tr><td>T<\/td><td>T<\/td><td>T<\/td><\/tr><tr><td>T<\/td><td>F<\/td><td><\/td><\/tr><tr><td>F<\/td><td>T<\/td><td><\/td><\/tr><tr><td>F<\/td><td>F<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fill&nbsp;in the third column. Determine if the values of both&nbsp;r&nbsp;and&nbsp;q&nbsp;are&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047578900_604\" class=\"wp-block-table\"><table><tbody><tr><td>q<\/td><td>r<\/td><td>r\u2227q<\/td><\/tr><tr><td>T<\/td><td>T<\/td><td>T<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><tr><td><strong>F<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><tr><td><strong>F<\/strong><\/td><td><strong>F<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/89897\/228\/744\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image.png\" alt=\"This image has an empty alt attribute; its file name is Worksheet-1-3-153.png\" class=\"wp-image-10251\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/90062\/495\/256\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-172.png\" alt=\"\" class=\"wp-image-7460\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-172.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-172-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-172-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Truth tables Key Notes: What is a Truth Table? Basic Logic Values Common Logical Operators Operator Symbol Meaning NOT \u00ac or ~ Reverses the truth value AND \u2227 True only if both values are true OR \u2228 True if at least one is true Truth Tables for Basic Operations A. NOT (\u00acA) A \u00acA T<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/w-3-truth-tables\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.3 Truth tables&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-425","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/425","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=425"}],"version-history":[{"count":10,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/425\/revisions"}],"predecessor-version":[{"id":17683,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/425\/revisions\/17683"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}