Relations and Functions — Course Quiz

A relation that is reflexive, symmetric and transitive is called

A a universal relation

B an empty relation

C a bijection

D an equivalence relation

On the set of lines in a plane, the relation \"is perpendicular to\" is

A reflexive and symmetric only

B an equivalence relation

C symmetric but neither reflexive nor transitive

D transitive only

On

A = \{1, 2, \ldots, 8\}

,

R = \{(a, b) : \lvert a - b \rvert \text{ is even}\}

. How many equivalence classes are there?

A

1

B

2

C

8

D

4

The function

f : \mathbf{R} \to \mathbf{R}

,

f(x) = x^2 + 4

is

A bijective

B onto but not one-one

C one-one but not onto

D neither one-one nor onto

The function

f : \mathbf{R} \to \mathbf{R}

,

f(x) = 2x + 9

is

A neither one-one nor onto

B onto but not one-one

C one-one but not onto

D bijective

How many onto functions are there from

\{1, 2, 3\}

to

\{p, q\}

?

A

6

B

9

C

2

D

8

If

f(x) = 2x + 1

and

g(x) = x^2

, what is

(f \circ g)(x)

?

A

4x^2 + 1

B

2x^2 + 1

C

2x^2 + 2x + 1

D

(2x + 1)^2

The inverse of

f : \mathbf{R} \to \mathbf{R}

,

f(x) = 6 - 2x

is

A

\displaystyle f^{-1}(y) = \dfrac{y - 6}{2}

B

\displaystyle f^{-1}(y) = \dfrac{y + 6}{2}

C

f^{-1}(y) = 6 + 2y

D

\displaystyle f^{-1}(y) = \dfrac{6 - y}{2}

For

f : [0, \infty) \to [3, \infty)

,

f(x) = x^2 + 3

, the inverse is

A

f^{-1}(y) = \sqrt{y} - 3

B

f^{-1}(y) = y^2 - 3

C

f^{-1}(y) = \sqrt{y + 3}

D

f^{-1}(y) = \sqrt{y - 3}

If

f

and

g

are invertible, then

(g \circ f)^{-1}

equals

A

g^{-1} \circ f^{-1}

B

f^{-1} \circ g^{-1}

C

f \circ g

D

g \circ f

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Relations and Functions — Course Quiz