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Question

If p and q are simple propositions, then pq is false when.


A

p is true and q is true

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B

pis false and q is true

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C

p is true and q is false

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D

Both p and q are false

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Solution

The correct option is C

p is true and q is false


Step-1: Definition of Conditional statement:

Conditional: Let p and qbe two propositions/statements then Conditional statement is defined as, if p is True and q is False then it gives output as False otherwise True for the remaining combinations.

It can be shown with the help of a truth table.

Notation: Conditional is denoted by the symbol .

Step-2: Truth table for pq

p

q

pq

T

T

T

T

F

F

F

T

T

F

F

T

Where T is True and F is False.

From the above table, we can conclude pq is False if pis True and q is False.

Hence option ‘C’ is correct.


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