AMSCO'S Geometry. New York - Rye High School

Conjunctions 43STEP 1. In the first column, we list the truth valuesof p. For each possible truth value ofp, there are two possible truth values forq. Therefore, we list T twice and F twice.pTTFFSTEP 2. In the second column, we list the truthvalues of q. In the two rows in which p istrue, list q as true in one and false in theother. In the two rows in which p is false,list q as true in one and false in the other.pTTFFqTFTFSTEP 3. In the last column, list the truth values ofthe conjunction, p ∧ q. The conjunction istrue only when both p and q are true.Theconjunction is false when one or bothconjuncts are false.p q p ∧ qT T TT F FF T FF F F The conjunction, p and q, is true only when both parts are true: p must betrue and q must be true.For example, let p represent “It is spring,” and let q represent “It is March.”CASE 1 Both p and q are true.On March 30, “It is spring” is true and “It is March” is true. Therefore, “It isspring and it is March” is true.CASE 2 p is true and q is false.On April 30, “It is spring” is true and “It is March” is false. Therefore, “It isspring and it is March” is false.CASE 3 p is false and q is true.On March 10, “It is spring” is false and “It is March” is true. Therefore, “It isspring and it is March” is false.CASE 4 Both p and q are false.On February 28, “It is spring” is false and “It is March” is false. Therefore,“It is spring and it is March” is false.