Homework SourseDiscrete Mathematics Question 18 SolutionWe use truth tables
Discrete Mathematics
Question 18
Solution
We use truth tables
(c)
From the above truth table, it is clear that (P Q)R and P(Q R ) have different truth values .
Hence (P Q)R and (PQ) ( PR ) are not equivalent
(d)
From the above truth table, it is clear that (P Q)R and P(Q R ) have same truth values .
Hence (P Q)R (PQ) ( PR )
(e)
From the above truth table, it is clear that (P Q)R and P(Q R ) have same truth values .
Hence (P Q)R P(QR )
( a )
From the above truth table, it is clear that P( QR) and (PQ) ( PR ) have same truth values .
Hence P( QR) (PQ) ( PR )
(b)
From the above truth table, it is clear that P( QR) and (PQ) ( PR ) have same truth values .
Hence P( QR) (PQ) ( PR )
| P | Q | R | PQ | (PQ)R | QR | P( QR) |
| F | F | F | T | F | T | T |
| F | F | T | T | T | T | T |
| F | T | F | T | F | F | T |
| F | T | T | T | T | T | T |
| T | F | F | F | T | T | T |
| T | F | T | F | T | T | T |
| T | T | F | T | F | F | F |
| T | T | T | T | T | T | T |
