Question

Consider the following compound statement,
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) $\sqrt{3}$ is a rational number or an irrational number,
(iii) $125$ is a multiple of $7$ or $8$
(iv) A rectangle is quadrilateral or a regular hexagon .
Which of the above statements is not true ?
A. (i)
B. (ii)
C. (iii)
D. (iv)

Answer 1

Hint: For this type question, first change all compound statements in simple statements or sentences. Then suppose P denotes the false statement and Q denotes the true statement after that check whether the compound statement is true or false.

Complete step-by-step answer:
For checking that the above statements are true or not, we should convert the compound statements in simple format one by one.
Denote P for false statement and Q for true statement.
The simple or compound statements of “Mumbai is the capital of Rajasthan or Maharashtra” are
(i) P:Mumbai is the capital of Rajasthan .
Q: Mumbai is the capital of Maharashtra.
It is clear that the compound statement is true.
The simple or compounds statements of “$\sqrt{3}$ is a rational number or an irrational number” are
(ii) P: $\sqrt{3}$ is a rational number.
Q: $\sqrt{3}$ is an irrational number.
It is clear from the statements that the compound statement is true.
The simple or compound statement of “ $125$ is a multiple of $7$ or $8$” are
(iii) P: $125$ is a multiple of$7$. .
Q: $125$ is multiple of $8$.
If we observe that both the components statements are false because $125$ is multiple of $5$. So that the given compound statement is false.
The simple or compound statement of” A rectangle is quadrilateral or a regular hexagon” are
(iv) P: A rectangle is a quadrilateral.
Q:A rectangle is a regular hexagon.
If we notice that P is true and Q is false so that the given compound statement is true.

Hence, from the above explanation it is clear that option C is correct.

Note: In such types of problems, students should know how to write compound statements . We can solve it by using a truth table with the help of logical connectors.
Logical connectors are <, >, ~, ->