{"id":427,"date":"2022-04-13T10:57:52","date_gmt":"2022-04-13T10:57:52","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=427"},"modified":"2025-04-08T12:22:37","modified_gmt":"2025-04-08T12:22:37","slug":"w-4-truth-values","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/w-4-truth-values\/","title":{"rendered":"W.4 Truth values"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"> <strong>Truth values<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-06b002f0ea72fc961b950791db3bb737\" style=\"color:#000060\"><strong>Definition of Truth Value<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">A <strong>truth value<\/strong> tells whether a statement is <strong>true (T)<\/strong> or <strong>false (F)<\/strong>.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Statement: &#8220;5 is greater than 2&#8221; \u2192 <strong>True<\/strong><\/li>\n\n\n\n<li>Statement: &#8220;The sky is green&#8221; \u2192 <strong>False<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-fde46be89084de02e43db57e97f8b880\" style=\"color:#000060\"><strong>Types of Statements<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Declarative Statements<\/strong>: These are statements that can be either true or false.<\/li>\n\n\n\n<li><strong>Not Truth-Bearing Statements<\/strong>: Questions, commands, or opinions do <strong>not<\/strong> have a truth value.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-7bed5eddcf8d6a803a83a10ea7f6470c\" style=\"color:#000060\"><strong>Symbols Used<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>T<\/strong> or <strong>1<\/strong> \u2192 for <strong>True<\/strong><\/li>\n\n\n\n<li><strong>F<\/strong> or <strong>0<\/strong> \u2192 for <strong>False<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-83423e10b896ac361a79ca6c294bb2e3\" style=\"color:#000060\"><strong>Use in Logic<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">Truth values are used in <strong>logic<\/strong> to analyze statements and arguments.<\/p>\n\n\n\n<p class=\"has-large-font-size\">They help in evaluating <strong>logical connectives<\/strong> like:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>AND (\u2227)<\/strong><\/li>\n\n\n\n<li><strong>OR (\u2228)<\/strong><\/li>\n\n\n\n<li><strong>NOT (\u00ac)<\/strong><\/li>\n\n\n\n<li><strong>IMPLIES (\u2192)<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4c45e43445e9eb984902c2eed9095812\" style=\"color:#000060\"><strong>Examples of Truth Values in Logical Statements<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>&#8220;2 + 2 = 4&#8221; \u2192 True<\/li>\n\n\n\n<li>&#8220;All birds can fly&#8221; \u2192 False (because some birds like ostriches cannot fly)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d75d7dc775d69524de0d1a1cd2d901c6\" style=\"color:#000060\"><strong>Negation and Truth Values<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">The <strong>negation<\/strong> of a true statement is false, and the negation of a false statement is true.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Statement: &#8220;The earth is round&#8221; \u2192 True<\/li>\n\n\n\n<li>Negation: &#8220;The earth is not round&#8221; \u2192 False<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-0bffb427f1c65ea20313d7c03f3d8c95\" style=\"color:#000060\"><strong>Truth Tables<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Truth tables are tools used to <strong>show all possible truth values<\/strong> of logical statements.<\/li>\n\n\n\n<li>Useful for understanding compound statements and logical operators.<\/li>\n<\/ul>\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-background has-large-font-size\" style=\"background-color:#f3ecd3\"><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-87099307f246a779dd7efb7937fc5ebe\" style=\"color:#b00012\">  \u2708\ufe0f <strong>If&nbsp;p&nbsp;is true, what is the truth value of&nbsp;~p?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>true<\/li>\n\n\n\n<li>false<\/li>\n\n\n\n<li>cannot&nbsp;be&nbsp;determined<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start&nbsp;by constructing a truth table that has only the row in which&nbsp;p&nbsp;is&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677046317749_569\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>~p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next,&nbsp;fill in the second column. Find the opposite of the value of&nbsp;p.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677046317749_564\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>~p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Finally,&nbsp;look at the truth value in the&nbsp;~p&nbsp;column.&nbsp;~p&nbsp;is&nbsp;<strong>false<\/strong>.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d3f4f3\"><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-7965c6078ae355fde6858e9b41327ca2\" style=\"color:#b00012\"> \u2708\ufe0f<strong> If&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is false, what is the truth value of&nbsp;q\u2228p?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>true<\/li>\n\n\n\n<li>false<\/li>\n\n\n\n<li>cannot&nbsp;be&nbsp;determined<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start&nbsp;by constructing a truth table that has only the row in which&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is&nbsp;false.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677046895250_487\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>q\u2228p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next,&nbsp;fill in the third column. Determine if the value of either&nbsp;q&nbsp;or&nbsp;p&nbsp;is&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677046895250_555\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>q\u2228p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>F<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Finally,&nbsp;look at the truth value in the&nbsp;q\u2228p&nbsp;column.&nbsp;When&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is false,&nbsp;q\u2228p&nbsp;is&nbsp;<strong>true<\/strong>.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dfe0fa\"><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-151bb1bbd35ebd22f547dac2c2273fa3\" style=\"color:#b00012\"> \u2708\ufe0f<strong>If&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is true, what is the truth value of&nbsp;q\u2227p?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>true<\/li>\n\n\n\n<li>false<\/li>\n\n\n\n<li>cannot&nbsp;be&nbsp;determined<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start&nbsp;by constructing a truth table that has only the row in which&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047012898_487\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>q\u2227p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next,&nbsp;fill in the third column. Determine if the values of both&nbsp;q&nbsp;and&nbsp;p&nbsp;are&nbsp;true.<\/li>\n<\/ul>\n\n\n\n<figure id=\"yui_3_18_1_1_1677047012898_555\" class=\"wp-block-table\"><table><tbody><tr><td>p<\/td><td>q<\/td><td>q\u2227p<\/td><\/tr><tr><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><td><strong>T<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Finally,&nbsp;look at the truth value in the&nbsp;q\u2227p&nbsp;column.&nbsp;When&nbsp;p&nbsp;is true and&nbsp;q&nbsp;is true,&nbsp;q\u2227p&nbsp;is&nbsp;<strong>true<\/strong>.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<strong>\ud83d\udd8a\ufe0f<\/strong><\/p>\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\/89995\/007\/133\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-154.png\" alt=\"\" class=\"wp-image-7463\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-154.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-154-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-154-150x150.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\/90063\/587\/568\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-173.png\" alt=\"\" class=\"wp-image-7464\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-173.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-173-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-173-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Truth values Key Notes: Definition of Truth Value: A truth value tells whether a statement is true (T) or false (F). Example: Types of Statements: Symbols Used: Use in Logic: Truth values are used in logic to analyze statements and arguments. They help in evaluating logical connectives like: Examples of Truth Values in Logical Statements:<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/w-4-truth-values\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.4 Truth values&#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-427","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/427","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=427"}],"version-history":[{"count":14,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/427\/revisions"}],"predecessor-version":[{"id":17694,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/427\/revisions\/17694"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}