Compound+Sentences

[|Youtube Video-Compound Sentences] Compound Sentences- A sentence composed of two or moe sentences joined together with //and// or //or. e.g.// When attempting to determine the truth value of a compound sentence, first determine the truth value of each of the components of the sentence. Let's examine examples number 1 and 2.
 * 1) "21 is divisible by 3 //and// 21 is not prime."
 * 2) "45 is a multiple of 9 or  13 - 20 = 7."
 * 3) " //If// 4 + 6 = 10 //and// 3 + 3 = 9, //then// all rectangles are squares."

** EXAMPLES: **

1. Determine the truth value of:  "21 is divisible by 3  // and    // 21 is not prime." "21 is divisible by 3"  (true) "21 is not prime"   (true) ||^  ||  Answer: The compound sentence (statement) is <span style="color: rgb(255,0,0);">true. <span style="color: #0e0c0c; font-family: 'Times New Roman', Times, serif;">
 * Substitute the truth values for the facts: ||   || <span style="color: rgb(255,0,0);"> T //and// T  || ||
 * Simplify the conjunction (<span style="color: rgb(255,0,0);">//and// ): ||  || <span style="color: rgb(255,0,0);"> T

QUIZ: Solve each open sentence and graph its solution set 1. 3x + 7 __<__ 1 2. a + 3 __>__ 6(a -7) 3. -3 < 2d + 1 < 7


 * EXAMPLES:**

"13 - 20 = 7"  (false)   || Substitute the truth values for the facts: ||   ||  T //or// F  ||   ||
 * 2.  Determine the truth value of:  "45 is a multiple of 9  //  or  //    13 - 20 = 7."   ||
 * "45 is a multiple of 9"     (true)
 * Simplify the disjunction ( //or// ): ||  ||  T  ||^   ||
 * Answer: The compound sentence (statement) is true . ||   ||

"  //If//     4 + 6 = 10    //  and    //  3 + 3 = 9,     //then//     all rectangles are squares." ||  "3 + 3 = 9"   (false) "  all rectangles are squares." (false) || Substitute the truth values for the facts: ||  ||  //if// (T //and// F) //then// F  || ||
 * 3.  Determine the truth value of:
 * "4 + 6 = 10 "    (true)
 * Simplify the conjunction (AND) first: ||  ||  //if// F //then// F  ||
 * Simplify the conditional: ||  ||  T
 * Answer: The compound sentence (statement) is true  ||

SOME HELPFULL LINKS: http://www.regentsprep.org/Regents/math/compsent/Lcompsen.htm http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Compound-Inequalities.topicArticleId-38949,articleId-38862.html http://www.math-videos-online.com/solve-compound-inequality.html A compound sentence such as 2 < 3 and 3 < 5 that is formed by joining two sentences with the word and is called a conjunction of sentences, and is true if and only both sentences are true. For example, the conjunction 2 <3 and 3< 5 is true, while the conjunction 2 < 3 and 5 < 3 is false, because 5 < < 3 false. A sentence such as 3 < 5 or 3 = 5 is called a disjunction of sentences. For a disjunction to be true, at least one of the joined sentences must be true. Disjunctions such as "3 <5 or 3 = 5" are read "5 is greater than or equal to 3".

QUIZ ANSWERS OF 1. {x:x __<__ -2} 2. {a:a __<__ 9} 3. {g:g__< 4/3}__