Question

The disjunction of the statements “Hyderabad is in India; $2 + 2 = 4$”, is
A) Hyderabad is in India and $2 + 2 = 4$
B) Hyderabad is in India or $2 + 2 = 4$
C) Hyderabad is in India but not $2 + 2 = 4$
D) Hyderabad is not in India or $2 + 2 = 4$

Answer 1

First we see that the truth-value would be true if both the statements are to be evaluated true and are false when both of the statements are false, we will check for both the statements to find the required disjunction.

Complete step by step solution:
We are given that the statement is “Hyderabad is in India; $2 + 2 = 4$”.
We need to find disjunction of these given statements.
We know that the disjunction of the two statements is the compound statement formed by joining two statements with the connector OR, AND, etc. and is the relation alternatives where either one or both of them are correct.
So these two alternatives are joined by logical connective “or”.
Here, both statements are correct so we have to see in which option they are joined by the connective “or”.
Considering option A, we will see that “Hyderabad is in India and $2 + 2 = 4$” are the two statements joined by ‘and’ which is the logical connective for conjunction.
So, it is an incorrect option.
Considering option B, we see that “Hyderabad is in India or $2 + 2 = 4$” are the two statements joined by logical connective ‘or’.

Hence, option B is correct.

Note:
All statements have truth-value if both of the statements need to be true for the “OR” statement is true, else false. The conjunction of two statements is a statement, which is true only when both the statements are correct and is false when either one of them or both of them are false. In conjunction, the two statements are joined by logical connective ‘’and”.