EXERCISE 3.1
Construct the truth table for the statement(¬p)^q.
| P | q | ¬p | (¬p)^q |
| T | T | F | F |
| T | F | F | F |
| F | T | T | T |
| F | F | T | F |
EXERCISE 3.2
By constructing the truth table, show that ¬(¬p) is logically equivalent to p.∨
| P | ¬p | ¬(¬p) |
| T | F | T |
| F | T | F |
EXERCISE 3.3
Construct the truth tables for p⇒(q∨r).Is the statement logically equivalent to (p⇒q)∨(p⇒r)
| p | q | r | q∨r | P⇒( q∨r) | p ⇒q | p⇒r | (p ⇒q)∨(p⇒r) |
| T | T | T | T | T | T | T | T |
| T | T | F | T | T | T | F | T |
| T | F | T | T | T | F | T | T |
| F | T | T | T | T | T | T | T |
| F | F | T | T | T | T | T | T |
| F | T | F | T | T | T | T | T |
| T | F | F | F | F | F | F | F |
| F | F | F | F | T | T | T | T |
EXERCISE 3.4
Write down the converse of the following statement
Q. If n is the multiple of 3 then n is not the multiple of 7
Ans: If n is not the multiple of 7 then n is the multiple of 3.
EXERCISE 3.5
Write down the contrapositive forms of the statements
Q. If n is a multiple of 7 then n is not a multiple of 3
Ans: If n is a multiple of 3 then n is not a multiple of 7
Q. If n is a multiple of 12 then n is a multiple of 4
Ans: If n is not a multiple of 4 then n is not multiple of 12.
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