Question

# If A={1,2,3,4}., then number of statements from the below having truth value as  true is (1) ∃ x∈A such that x+3=8  (2) ∀ x∈A,x+2<7. (3) ∀ x∈A such that x+1<3. (4) ∀ x∈A,x+3≥5.

Solution

## (1) Clearly, no number in A satisfies x+3=8. ∴ the given statement is false. (2) Every number in A satisfies x+2<7. So, given statement is true. (3) Clearly, x=4∈A doesnot satisfies x+1<3. ∴ the given statement is false. (4) Since x=1∈A does not satisfy x+3≥5, the statement is false. Clearly we can say that we have 2 true statements.

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