Question

If a compound statement is made up of three simple statements, then the number of rows in the truth table is
a.8
b.6
c.4
d.2

Answer 1

Hint: Use the concept i.e. “If a compound statement is made up of n simple statements, then the number of rows in the truth table will be ${{2}^{n}}$.” And put the value of the number of statements to get the final answer.

Complete step by step answer:
To solve the above problem assume the three simple statements to be P, Q, and R respectively and the compound statement is made up of these three simple statements.
As we have to find the number of rows in the truth table therefore ultimately we have to find the different number of arrangements of Truth Values i.e. ‘True’ and ‘False’ for these three simple statements and to find that we should know the concept given below,
Concept:
If a compound statement is made up of n simple statements, then the number of rows in the truth table will be ${{2}^{n}}$.
As the given compound statement is made up of three simple statements therefore by using the concept given above we can write the number of rows in the truth table as,
Number of rows in the truth table = ${{2}^{3}}$
Therefore, number of rows in the truth table = 8
For simplicity we will write the different combinations in the truth table therefore we will get,

For simplicity we will write the different combinations in the truth table therefore we will get,

p	q	r
T	T	T
T	T	F
T	F	T
T	F	F
F	T	T
F	T	F
F	F	T
F	F	F

As shown in the above truth table there are a total 8 rows in the truth table containing a compound statement which consists of three simple statements.
Therefore the correct answer is option (a).

Note: Always try to write the truth table if you are writing a descriptive answer for full marks otherwise if you are solving it in a competitive exam then there is no need to cross check your answer as you have very less time.