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Truth value of compound statements made of mathematical facts

This type of question, asked 9 times: May 2022 S1, 9 May 2023 S1, 15 May 2023 S2, 19 Apr 2025 S1, 22 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S2, 20 Apr 2026 S1, 20 Apr 2026 S2. All 9 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    103
    If p: ∀n∈N\forall n \in \mathbb{N}, n2+nn^2+n is an even number; q: ∀n∈N\forall n \in \mathbb{N}, n2−nn^2-n is an odd number, then the truth values of p∧qp \wedge q, p∨qp \vee q and p→qp \rightarrow q are respectively

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  2. Question 2

    9 May 2023 S1

    118
    Consider the statements: (A) If 3+3=73+3=7, then 4+3=84+3=8. (B) If 5+3=85+3=8, then earth is flat. (C) If both (A) and (B) are true, then 5+6=175+6=17. Then which of the following statements is correct?

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  3. Question 3

    15 May 2023 S2

    145
    If p: The total prime numbers between 2 to 100 are 26. q: Zero is a complex number. r: Least common multiple (L.C.M.) of 6 and 7 is 6. Then which of the following is correct?

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  4. Question 4

    19 Apr 2025 S1

    148
    Consider the three statements p:∀n∈N,10n−3p:\forall n \in\mathbb{N},10n - 3 is a prime number, when n is not divisible by 3 . q:23,−23,−13q:\frac{2}{\sqrt{3}},\frac{- 2}{\sqrt{3}},\frac{- 1}{\sqrt{3}} are the direction cosines of a directed line. r:sin⁡xr:\sin x is an increasing function in the interval [−π2,π2]\left\lbrack \frac{-\pi}{2},\frac{\pi}{2} \right\rbrack. Then which of the following statement pattern has truth value true?

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  5. Question 5

    22 Apr 2025 S1

    121
    Which of the following statements has the truth value T? (A) cube roots of unity are in Geometric progression and their sum is 1 (B)  4+7>10\ 4 + 7 > 10 iff 2+8<102 + 8 < 10 (C)  ∃x∈N\ \exists x \in \mathbb{N} such that x2−3x+2=0x^{2} - 3x + 2 = 0 and ∃n∈N\exists n \in \mathbb{N} such that n is an odd number (D) 3+i3 + i is a complex number or 2+3=5\sqrt{2} + \sqrt{3} = \sqrt{5}

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  6. Question 6

    25 Apr 2025 S2

    105
    Consider the following three statements (A) If 3+2=73 + 2 = 7 then 4+3=84 + 3 = 8. (B) If 5+2=75 + 2 = 7 then earth is flat. (C) If both (A) and (B) are true then 5+6=115 + 6 = 11. Which of the following statements is correct?

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  7. Question 7

    26 Apr 2025 S2

    107
    If p,q,r,sp, q, r, s are statements where p:A2−B2=(A−B)(A+B)p: A^{2}-B^{2}=(A-B)(A+B) for matrices A,BA, B with AB≠BAAB \neq BA; q:5≤5q: 5 \leq 5; r:8C1+8C2+8C3+⋯+8C8=256r: {}^{8}C_{1}+{}^{8}C_{2}+{}^{8}C_{3}+\cdots+{}^{8}C_{8}=256; s:s: the maximum value of 8Cr{}^{8}C_{r} is 70, then the statement from the following having truth value true is

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  8. Question 8

    20 Apr 2026 S1

    64
    Which of the following is/are not true ? I) If 1 is not a prime number, then 2 is not a prime number. II) e is a vowel and 12×3=3612 \times 3 = 36 III) It is not true that 14 is a composite number and 3 is even number. IV) 5\sqrt{5} is an irrational number, but 3+53 + \sqrt{5} is a complex number.

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  9. Question 9

    20 Apr 2026 S2

    51
    The statement having truth value 'T' from the following is

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