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Truth value of quantified statements over a given set

This type of question, asked 4 times: 11 Apr 2026 S1, 11 Apr 2026 S2, 17 Apr 2026 S2, 15 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    11 Apr 2026 S1

    51
    If A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\}, then which of the following statements is not true?

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  2. Question 2

    11 Apr 2026 S2

    62
    If A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\} then which of the following is not true?

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  3. Question 3

    17 Apr 2026 S2

    58
    Which of the following statements is/are False? S1:∃n∈NS_1 : \exists n \in N, such that n2+n+2n^2 + n + 2 is divisible by 4. S2:∃x∈NS_2 : \exists x \in N, such that x−17<20x - 17 < 20. S3:∀n∈N,x2+3x−10=0S_3 : \forall n \in N,\quad x^2 + 3x - 10 = 0. S4:∀n∈N,n2≥1S_4 : \forall n \in N,\quad n^2 \ge 1.

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  4. Question 4

    15 May 2026 S2

    67
    Let A={1,2,3,…,10}A = \{1, 2, 3, \ldots, 10\}. Consider the following statements: p:∀x∈A, x2−x>0p : \forall x \in A,\ x^2 - x > 0 q:∃x∈Aq : \exists x \in A, such that x+10=20x + 10 = 20 Then the truth values of pp and qq are respectively ____

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