MCQs of Set Theory (Discrete Mathematics - 3140708)

Discrete Mathematics (3140708) MCQs

MCQs of Set Theory

Showing 31 to 40 out of 70 Questions

31.

If f = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} then Range(f)= _____.

(a)	{2, 4, 6, 8, 10, 12, 14}
(b)	{1, 2, 3, 4, 5, 6, 7}
(c)	A and B both
(d)	none of the above

32.

$If f (x) = \{\begin{cases} x; x \geq 0 \\ - x; x < 0 \end{cases} for f : ℝ \to ℝ$ then f is known as _____ function.

(a)	modulus
(b)	constant
(c)	identity
(d)	ceiling

33.

$If f (x_{1}) = f (x_{2}) \Rightarrow x_{1} = x_{2}, \forall x_{1}, x_{2} \in A for f : A \to B$ then f is said to be which function?

(a)	one to one
(b)	onto
(c)	surjective
(d)	bijective

34.

In usual notation, ${(g \circ f)}^{- 1} (x) =_____.$

(a)	$(g^{- 1} \circ f^{- 1}) (x)$
(b)	$(g^{- 1} \circ f) (x)$
(c)	$(g \circ f^{- 1}) (x)$
(d)	$(f^{- 1} \circ g^{- 1}) (x)$

35.

f : A \to B

has the inverse

g : B \to A

if and only if f is _____.

(a)	one to one
(b)	onto
(c)	both A and B
(d)	none of these

36.

Let $f : ℝ \to ℝ, f (x) = x + 2$ then $f^{- 1} (x) =$ _____.

(a)	$x + 2$
(b)	$x - 2$
(c)	x
(d)	2

37.

Let X={1, 2, 3} and f & g are functions from X to X given by f={(1, 2),(2, 3),(3, 1)} and g={(1, 2),(2, 1),(3, 3)} then the function $(g \circ f)^{- 1} (x)$ =_____.

(a)	{(1, 1),(2, 2),(3, 3)}
(b)	{(1, 1),(2, 3),(3, 2)}
(c)	{(1, 2),(2, 1),(3, 3)}
(d)	{(1, 2),(2, 3),(3, 1)}

38.

Let X={1, 2, 3} and f, g & h are functions from X to X given by f={(1, 2), (2, 3), (3, 1)}, g={(1, 2), (2, 1), (3, 3)} & h={(1, 1), (2, 2), (3, 1)}. The function

f \circ h \circ g

=_____.

(a)	{(1, 1), (2, 2), (3, 3)}
(b)	{(1, 3), (2, 2), (3, 1)}
(c)	{(1, 3), (2, 2), (3, 2)}
(d)	{(1, 3), (2, 1), (3, 2)}

39.

Let f(x)=x+2, g(x)=x-2 and h(x)=3x,

\forall x \in ℝ \Rightarrow f \circ h \circ g

=_____.

(a)	3x-1
(b)	3x-2
(c)	3x-3
(d)	3x-4

40.

Let

f : ℝ \to ℝ, f (x) = - x^{2}

and

g : ℝ^{+} \to ℝ^{+}, g (x) = \sqrt{x}

. Then

f \circ g (x)

=_____.

(a)	x
(b)	-x
(c)	$x^{2}$
(d)	$- x^{2}$

Showing 31 to 40 out of 70 Questions