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Discrete Mathematics | Identity and Composition of Functions MCQs

Discrete Mathematics | Identity and Composition of Functions MCQs: This section contains multiple-choice questions and answers on Identity and Composition of Functions in Discrete Mathematics.
Submitted by Anushree Goswami, on July 17, 2022

1. When every element of set A has a copy of itself, it is called the identity function, f (a) = ___?

1. a ∀ A ∈ a
2. A ∈ A
3. a ∀ A ∈ A
4. a ∀ a ∈ A

Answer: D) a ∀ a ∈ A

Explanation:

When every element of set A has a copy of itself, it is called the identity function, f (a) = a ∀ a ∈ A.

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2. Identity function is denoted by the symbol -?

1. ID
2. I
3. U
4. T

Answer: B) I

Explanation:

Identity function is denoted by the symbol I.

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3. If f: X -> Y is a _____ function, it is invertible?

1. Dijective
2. Discretive
3. Bijective
4. Bipolar

Answer: C) Bijective

Explanation:

If f: X -> Y is a bijective function, it is invertible.

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4. If f^-1 is a function from ___, there is an inverse function for f?

1. X to Y
2. X to X
3. Y to X
4. Y to Y

Answer: C) Y to X

Explanation:

If f^-1 is a function from Y to X, there is an inverse function for f.

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5. g [f(x)] is known as -?

1. gox
2. gof
3. gfx
4. gxf

Answer: B) gof

Explanation:

g [f(x)] is known as gof.

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6. _____ if f is A -> B and g is B -> C, which means composition of f with g is a function from A into C?

1. (gof) (y) = g [f(x)]
2. (gof) (x) = g [f(y)]
3. (gof) (x) = g [x(x)]
4. (gof) (x) = g [f(x)]

Answer: D) (gof) (x) = g [f(x)]

Explanation:

(gof) (x) = g [f(x)] if f is A -> B and g is B -> C, which means composition of f with g is a function from A into C.

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7. It is necessary to ____ in order to find the composition of f and g?

1. find the image of f(x) under f before finding the image of f (x) under g
2. find the image of x under f before finding the image of f (x) under f
3. find the image of x under g before finding the image of f (x) under g
4. find the image of x under f before finding the image of f (x) under g

Answer: D) find the image of x under f before finding the image of f (x) under g

Explanation:

It is necessary to find the image of x under f before finding the image of f (x) under g in order to find the composition of f and g.

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8. The function (gof) (gof) is _____ if f and g are one-to-one?

1. One-to-one
2. One-to-many
3. Many-to-one
4. Many-to-many

Answer: A) One-to-one

Explanation:

The function (gof) (gof) is also one-to-one if f and g are one-to-one.

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9. Functions (gof) (gof) are onto if f and g are ___?

1. Into
2. Onto
3. To
4. None

Answer: B) Onto

Explanation:

Functions (gof) (gof) are onto if f and g are onto.

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10. There is no commutative property in composition, but ____ property is present consistently?

1. Associative
2. Identity
3. Duplicative
4. None

Answer: A) Associative

Explanation:

There is no commutative property in composition, but associative property is present consistently.

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