Mathematical Reasoning CBSE Questions & Answers

Mathematical Reasoning

This is Mathematics Class 11 Mathematical Reasoning CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
\( \sim p \vee \sim q\)is logically equivalent to
  • A
    \( \sim p \to \sim q\)
  • B
    \(p \to \sim q\)
    Correct
  • C
    \(p \leftrightarrow q\)
  • D
    \(p \to \sim q\)
2
\( \sim (p \wedge q)\) is logically equivalent to
  • A
    \( \sim p \leftrightarrow \sim q\)
  • B
    \( \sim p \vee \sim q\)
    Correct
  • C
    \( \sim p \to \sim q\)
  • D
    \( \sim p \to q\)
3
Which of the following is logically equivalent to \(p \leftrightarrow q\) ?
  • A
    \((p \to q) \wedge (q \to p)\)
    Correct
  • B
    \((p \wedge q) \wedge (q \to p)\)
  • C
    \((p \wedge q) \wedge (q \vee p)\)
  • D
    \((p \to q) \vee (q \to p)\)
4
If \(p \to (q \vee r)\) is false , then the truth values of p , q , r are respectively
  • A
    F,T,T
  • B
    T,T,F
  • C
    T,F,F
    Correct
  • D
    F,F,F
5
The compound statement \(p \to ( \sim p \vee q)\) is false , then the truth values of p and q are respectively
  • A
    F,F
  • B
    T,F
    Correct
  • C
    F,T
  • D
    T,T
6
The false statement in the following is
  • A
    )\((p \to q) \leftrightarrow ( \sim q \to \sim p)\)is a contradiction
    Correct
  • B
    \(p \wedge \sim p\) is a contradiction
  • C
    \(p \vee \sim p\) is a tautology
  • D
    \( \sim ( \sim p) \leftrightarrow p\) is a tautology
7
Which of the following is not a proposition ?
  • A
    5 is an even integer
  • B
    \(\sqrt 2 \) is irrational
  • C
    3 is a prime
  • D
    Mathematics is interesting
    Correct
8
\((p \wedge \sim q) \wedge ( \sim p \vee q)\) is
  • A
    both a tautology and a contradiction
  • B
    a tautology
  • C
    neither a tautology nor a contradiction
  • D
    a contradiction
    Correct
9
The proposition \((p \to \sim p) \wedge ( \sim p \to p)\) is
  • A
    a contradiction
    Correct
  • B
    both a tautology and a contradiction
  • C
    neither a tautology nor a contradiction
  • D
    a tautology
10
Which of the following statement is a tautology
  • A
    \((p \vee \sim q) \wedge (p \vee q)\)
  • B
    \(( \sim p \vee \sim q) \vee (p \vee q)\)
    Correct
  • C
    \(( \sim p \vee q) \sim (p \vee \sim q)\)
  • D
    \(( \sim p \vee \sim q) \to (p \vee q)\)
11
Negation of the statement \(p \to (q \wedge r)\) is
  • A
    \(p \wedge ( \sim q \vee \sim r)\)
    Correct
  • B
    \(p \to ( \sim q \vee r)\)
  • C
    \( \sim p \to ( \sim q \vee r)\)
  • D
    \( \sim p \wedge ( \sim q \vee \sim r)\)
12
Negation of the statement \((p \wedge r) \to (r \vee q)\) is
  • A
    \((p \wedge r) \vee (r \to q)\)
  • B
    \((p \wedge r) \vee ( \sim r \to \sim q)\)
  • C
    \((p \wedge r) \wedge ( \sim r \wedge \sim q)\)
    Correct
  • D
    \((p \wedge r) \wedge ( \sim r \to \sim q)\)
13
Negation of the statement \(q \vee \sim (p \wedge r)\) is
  • A
    \( \sim q \wedge \sim (p \wedge r)\)
  • B
    \( \sim q \wedge (p \wedge r)\)
    Correct
  • C
    \( \sim q \vee (p \wedge r)\)
  • D
    \( \sim q \to \sim (p \wedge r)\)
14
Which of the following is always true ?
  • A
    \((p \to q) \cong ( \sim q \to \sim p)\)
    Correct
  • B
    \( \sim (p \vee q) \cong ( \sim p \vee \sim q)\)
  • C
    \( \sim (p \wedge q) \cong ( \sim p \wedge \sim q)\)
  • D
    \( \sim (p \to q) \cong (p \vee \sim q)\)
15
Negation of the statement \( \sim p \to (q \vee r)\) is
  • A
    \( \sim p \wedge ( \sim q \wedge \sim r)\)
    Correct
  • B
    \(p \vee (q \wedge r)\)
  • C
    \(p \wedge (q \vee r)\)
  • D
    \(p \to \sim (q \vee r)\)