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Mathematical Reasoning Test - 7

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Mathematical Reasoning Test - 7
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  • Question 1
    1 / -0

    Let p be the proposition : Mathematics is interesting and let q be the proposition that Mathematics is difficult, then the symbol p ∧  q means 

    Solution

    using connective and for ∧

  • Question 2
    1 / -0

    The negation of the compound statement p ∨ (∼ p ∨ q) is

    Solution

    ∼(p  ∨ (∼ p ∨ q ) ) ≡ ∼p ∧ (p ∧ ∼ q)    Applying De morgan's law

  • Question 3
    1 / -0

    ∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to

    Solution

    (∼  p ∧ ∼  q ) ∨ ( ∼ p ∧ q )   Rules of neagtion

    ∼p ∧ (  ∼ q ∨ q)     Associative law

    ∼p ∧ T

    ∼p

  • Question 4
    1 / -0

    The proposition p → ∼ (p ∧ ∼ q ) is

    Solution
    p q ∼q∼q ∼(p∧∼q) p→(p∧∼q)
    T T F T T
    T F T F F
    F T F T T
    F F T T T

    since proposititon has both T and F.hence option a

  • Question 5
    1 / -0

    The proposition (p →∼ p ) ∧ (∼ p → p) is

    Solution

    it can be simplified as p ↔ ∼ p   since ( p →  q ) ∧ ( q → p ) ≡ p ↔ q

    F  (T ↔ F ≡ F     and  F↔ T ≡ F )

  • Question 6
    1 / -0

    The contrapositive of If 2x + 3 = 9  then x≠4 is

    Solution

    p: 2x + 3 = 9  q:x=4 .The contrapositive of p → q is ∼ q →  ∼ p

  • Question 7
    1 / -0

    Which of the following is equivalent to (p ∧ q) ?

    Solution

    p ∧ q Since ∼( p →  q) ≡ p ∧ ∼ q

  • Question 8
    1 / -0

    The negative of the statement: "Plant take in CO2 and do not give out O2" is

    Solution

    Plant do not take in CO2 and do not O2.

  • Question 9
    1 / -0

    Which of the following is logically equivalent to ∼ (p ↔ q) ?

    Solution

    ∼ (  p ↔  q ) ≡ ( p ∧ ∼ q ) ∨ ( q ∧ ∼ p)

  • Question 10
    1 / -0

    p →  q is logically equivalent to

    Solution

    p → q ≡ ∼ p ∨ q   eq 1

    ∼ q → ∼ p ≡ q ∨ ∼ p  eq 2

    hence from 1 and 2 both are equal

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