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

  • [(pĀ ā‡’ q)Ā ^ q]Ā ā‡’ q
  • [(pĀ ā‡’ q)Ā ^ q]Ā ā‡”Ā q
  • [(pĀ ā‡’ q)Ā ^ q]Ā ^Ā q checkmark
  • [(pĀ ā‡’ q)Ā ^ q] vĀ ~Ā q

The correct answer is: C

Explanation

p p p ā‡’ q (p ā‡’ q) āˆ§ q [(p ā‡’ q) āˆ§ q] ā‡’ q [(p ā‡’ q) āˆ§ q] ā‡” q [(p ā‡’ q) āˆ§ q] āˆ§ q

[(p ā‡’ q) āˆ§ q] āˆØ āˆ¼ q
T F F F T T F T

From the truth table above, [(p ā‡’ q) āˆ§ q] āˆ§ q is FALSE.

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