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construct a truth table for the given statement ((
eg qland p)vee(qland p)
complete the truth table.
p q (
eg q) (
eg qland p) (qland p) ((
eg qland p)vee(qland p)
t t f f t t
t f f t t t
Step1: Analyze when p = F, q = T
When p is False (F) and q is True (T), ~q is False (F). Then ~q ∧ p is False (F) because for a conjunction (∧), both operands must be True, and here one is False. q ∧ p is False (F) for the same reason. Then for the disjunction (∨) of ~q ∧ p and q ∧ p, since both are False, (~q ∧ p) ∨ (q ∧ p) is False (F).
Step2: Analyze when p = F, q = F
When p is False (F) and q is False (F), ~q is True (T). But ~q ∧ p is False (F) because p is False. q ∧ p is False (F) as well. So, (~q ∧ p) ∨ (q ∧ p) is False (F) since both parts of the disjunction are False.
| p | q | ~q | ~q ∧ p | q ∧ p | (~q ∧ p) ∨ (q ∧ p) |
|---|---|---|---|---|---|
| T | F | T | T | F | T |
| F | T | F | F | F | F |
| F | F | T | F | F | F |
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| p | q | ~q | ~q ∧ p | q ∧ p | (~q ∧ p) ∨ (q ∧ p) |
|---|---|---|---|---|---|
| T | F | T | T | F | T |
| F | T | F | F | F | F |
| F | F | T | F | F | F |