For statements P,Q, and R show that ((P ^ Q) => R) is logically equiv to ((P ^ (
ID: 2940725 • Letter: F
Question
For statements P,Q, and R show that
((P ^ Q) => R) is logically equiv to ((P ^ (~R)) => (~Q))
Your help is greatly appreciated.
Explanation / Answer
Truth tables and logic help! will rate lifesaver. Question Details For statements P,Q, and R show that ((P ^ Q) => R) is logically equiv to ((P ^ (~R)) => (~Q)) Your help is greatly appreciated. EQUATION EDITOR NOT WORKING. USING * FOR INTERSECTION , - FOR NEGATION...AND ...= FOR IMPLIED STATEMENT 1 FOR TRUE AND 0 FOR FALSE LET US MAKE THE LOGIC TABLES FOR BOTH OF THE ABOVE STATEMENTS HOPE YOU KNOW HOW TO MAKE THE TABLES FIRST PUT P,Q,R IN ALL POSSIBLE COMBINATIONS ..THERE WILL BE 2*2*2=8 VARIATIONS, SINCE EACH OF P,Q,R CAN HAVE 2 VALUES T OR F OR 1 AND 0. USE OF 1 AND O MAKES IT VERY EASY TO COMPILE INTERSECTION [AND UNION TOO WHICH IS JUST ADDITION OF VARIABLES ]WHICH IS JUST PRODUCT OF THE VARIABLES. NEGATION IS OBTAINED BY SUBTRACTING THE VARIABLE FROM 1 THE UNIVERSE. IMPLIED STATEMENT IS ....A IMPLIES B MEANS IF A IS TRUE B SHALL BE TRUE , B CAN NOT BE FALSE IN SUCH CASES....IF A IS FALSE THEN IT DOES NOT MATTER IF B IS TRUE OR FALSE..ACCORDINGLY WE GET TRUTH TABLE FOR P*Q=R P Q R P*Q P*Q=R 1 1 1 1 T 1 1 0 1 F 1 0 1 0 T 1 0 0 0 T 0 1 1 0 T 0 1 0 0 T 0 0 1 0 T 0 0 0 0 T TRUTH TABLE FOR P*(-R)=-Q P Q R -R -Q P*(-R) P*(-R)=-Q 1 1 1 0 0 0 T 1 1 0 1 0 1 F 1 0 1 0 1 0 T 1 0 0 1 1 1 T 0 1 1 0 0 0 T 0 1 0 1 0 0 T 0 0 1 0 1 0 T 0 0 0 1 1 0 T WE FINF THAT FOR A GIVEN SET OF CONDITIONS OF P,Q,R, THE TRUTH TABLES OF THE 2 STATEMENTS ARE IDENTICAL SO WE CONCLUDE THAT BOTH STATEMENTS ARE EQUIVALENT IF STILL IN DOUBT PLEASE COME BACK