MCQs of Review of Mathematical Theory (Theory of Computation - 3160704)

Theory of Computation (3160704) MCQs

MCQs of Review of Mathematical Theory

Showing 31 to 30 out of 40 Questions

31.

Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 3 and g(x) = 3x + 3. Then the composition of f and g is ____________

(a)	6x + 9
(b)	6x + 6
(c)	6x + 7
(d)	6x + 8

32.

Bijection fuction is_________

(a)	Equal to on to function
(b)	One to one and on to function
(c)	One to one or on to function
(d)	None of these

33.

The contrapositive of

p \to q

is:

(a)	$\neg p \to \neg q$
(b)	$q \to p$
(c)	$\neg q \to \neg p$
(d)	$\neg q \to p$

34.

The inverse of

p \to q

is:

(a)	$\neg p \to \neg q$
(b)	$q \to p$
(c)	$\neg q \to \neg p$
(d)	$\neg q \to p$

35.

The number 2.101001000100001... is

(a)	A natural number
(b)	A rational number
(c)	A whole number
(d)	An irrational number

36.

In the principle of mathematical induction, which of the following steps is compulsory?

(a)	Induction hypothesis
(b)	Inductive reference
(c)	Induction set assumption
(d)	Minimal set representation

37.

According to principle of mathematical induction, if

P (k + 1) = m^{(k + 1)} + 7

is true then _____ must be true.

(a)	$P (k) = 7 m^{(k)}$
(b)	$P (k) = m^{(k)} + 7$
(c)	$P (k) = m^{(k + 2)} + 7$
(d)	$P (k) = m^{(k)}$

38.

According to principle of mathematical induction, if P (k) = k(3k+4) is true then _____ must be true.

(a)	P(k+1)=(k+1)(3(k+1)+4)
(b)	P(k+1)=( k+1)((k+1)+4)
(c)	P(k)=(k+1)(3(k+1)+4)
(d)	P(k)=(k+1)((k+1)+4)

39.

Operation over the language is

(a)	Concatenation
(b)	Union
(c)	* (Kleene closure)
(d)	All of these

40.

What is the base case for the inequality

7^{n} > n^{3}

, where n = 3?

(a)	652 > 189
(b)	42 <= 431
(c)	42 < 132
(d)	343 > 27

Showing 31 to 30 out of 40 Questions