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In a truth table, if p is true and q is false, which of the...

Further Mathematics
WAEC 2024

In a truth table, if p is true and q is false, which of the following notations is false

  • A. [(p ⇒ q) ^ q] ⇒ q
  • B. [(p ⇒ q) ^ q] ⇔ q
  • C. [(p ⇒ q) ^ q] ^ q
  • D. [(p ⇒ q) ^ q] v ~ q
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Correct Answer: Option C
Explanation
p p p ⇒ q (p ⇒ q) ∧ q [(p ⇒ q) ∧ q] ⇒ q [(p ⇒ q) ∧ q] ⇔ q [(p ⇒ q) ∧ q] ∧ q

[(p ⇒ q) ∧ q] ∨ ∼ q
T F F F T T F T

From the truth table above, [(p ⇒ q) ∧ q] ∧ q is FALSE.

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