Question
~ P → ~ Q

Answer

Truth table:
Column $\rightarrow$ 1 2 3 4 5
Row $\downarrow$ P Q ~P ~ Q ~P $\rightarrow$ ~ Q
1 T T F F T
2 T F F T T
3 F T T F F
4 F F T T T
  1(~) 2 (~) 3, 4 ($\rightarrow$)
Explanation: ~ P → ~ Q in column no. 1 and 2 which are the pillars. While the remaining three are secondary columns. Column no. 5 presents the whole complex joint statement. Column no. 5 The following facts become clear:
(1) According to the first row, if P is truth and Q is truth, then ~ P → ~ Q is the whole statement truth.
(2) According to the second row, if P is true and Q is untrue, then ~ P → ~ Q is the whole statement is true.
(3) According to the third row, if P is untrue and Q is true, then ~ P → ~ Q is the whole statement is untrue.
(4) According to the fourth row, if P is untrue and Q is untrue, then ~ P → ~ Q is the whole statement is true.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free