Which of the following quantified statement is false?(A) ∃x ∈ N, – InterviewSolution

InterviewSolution

1.

Which of the following quantified statement is false?(A) ∃x ∈ N, such that x + 5 ≤ 6 (B) ∀x ∈ N, x2 \(\nleq\) 0 (C) ∃x ∈ N, such that x - 1 < 0 (D) ∃x ∈ N, such that x2 - 3x + 2 = 0

Answer»

Correct option: (C) ∃x ∈ N, such that x - 1 < 0

Option (C) is false, since for every natural number the statement x - 1 ≥ 0 is always true.

Discussion

No Comment Found

Related InterviewSolutions

Let p : A triangle is equilateral, q : A triangle is equiangular, then inverse of q → p is(A) If a triangle is not equilateral then it is not equiangular. (B) If a triangle is not equiangular then it is not equilateral. (C) If a triangle is equiangular then it is not equilateral. (D) If a triangle is equiangular then it is equilateral.
Negation of (~p → q) is(A) ~ p ∨ ~q (B) ~p ∧~ q (C) p ∧ ~ q (D) ~ p ∨ q
Write the negations of :All natural numbers are whole numbers.
Write the duals of (p ∨ q) ∨ c.
Write the negations of the x + 8 > 11 or y – 3 = 6
Write the negations of the 11 < 15 and 25 > 20
Write the negations of the :Qudrilateral is a square if and only if it is a rhombus.
Write the negations of the :It is cold and raining.
The statement, ‘If it is raining then I will go to college’ is equivalent to (A) If it is not raining then I will not go to college. (B) If I do not go to college, then it is not raining. (C) If I go to college then it is raining. (D) Going to college depends on my mood.
p → Ram is richq → Ram is successfulr → Ram is talentedWrite the symbolic form of the given statement.Ram is neither rich nor successful and he is not talented(A) ~p ∧ ~q ∨ ~r (B) ~p ∨ ~q ∧ ~r (C) ~p ∨ ~q ∨ ~r (D) ~p ∧ ~q ∧ ~r