Important Questions of Mathematical Reasoning Mathematics | Zigya

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41.

Contrapositive o the statement : 'If a function f is differentiable at a, then it is also continuous at a', is :

  • If a function f is not continuous at a, then it is not differentiable at a.

  • If a function f is continuous at a, then it is differentiable at a.

  • If a function f is not continuous at a. then it is differentiable at a.

  • If a function f is continuous at a, then it is not differentiable at a.


42.

The negation of the Boolean expression x  ~ y is equivalent to : 

  • ~ x  y  ~ x  ~ y

  • x  y  ~ x  ~ y

  • x  ~ y  ~ x  y

  • x  y  ~ x  ~ y


43.

The statement

p  q  p   p p  q is

  • equivalent to p  q  ~ p

  • a contradiction

  • a tautology

  • equivalent to p  q  ~ q


44.

The negation of the Boolean expression p v (~ p  q) is equivalent to :

  • p  ~ q

  • ~ p  q

  • ~ p  ~ q

  • ~ p  ~ q


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45.

Consider the statement: For an integer n, if n3  1 is even, then n is odd. The contrapositive statement of this statement is:

  • For an integer n, if n is even, then n3 – 1 is odd

  • For an integer n, if n is even, then n3 – 1 is even.

  • For an integer n, if n3 – 1 is not even, then n is not odd

  • For an integer n, if n is odd, then n3 – 1 is even.


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