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

Disjunction of two statements is true when either statement are true or both statements are true and is false when both the statements are false. First, check whether both the statements are correct or not. Then check if they are joined by “or” because in disjunction two alternatives are joined.

Complete step by step solution: Given statement is “Hyderabad is in India; $2 + 2 = 4$”
We have to find disjunction of this statement.
Since we already know that disjunction is the relation between two distinct 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 or.
In option A, “Hyderabad is in India and $2 + 2 = 4$” the two statements are joined by ‘and’ which is the logical connective for conjunction.
In option B, “Hyderabad is in India or $2 + 2 = 4$” the two statements are joined by logical connective ‘or’ hence this is the conjunction of the given statements.

Hence, the correct answer is B.

Note: 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 y logical connective ‘and’.