Sets — Multiple Choice Questions

A collection of beautiful flowers is a set:

1. Yes

2. No

3. none of these two

Answer

The word 'beautiful' is a relative term. A flower that is beautiful to one person may not be beautiful to another person. So, the objects are not well defined and the collection does not form a set.

Hence, option 2 is the correct option.

Set of integers between 5 and 6 is:

1. an infinite set

2. not an empty set

3. a singleton set

4. the empty set

Answer

There is no integer between 5 and 6. So, the set has no element, i.e. it is the empty set.

Hence, option 4 is the correct option.

Set A = Set B ⇒

1. A and B are equivalent sets

2. A and B have identical elements

3. A contains all the elements of B and B contains all the elements of A.

4. all of the above are true

Answer

If Set A = Set B, then both sets have exactly the same (identical) elements. This means A contains all the elements of B and B contains all the elements of A, and since the number of elements is also the same, A and B are equivalent too. So, all the given statements are true.

Hence, option 4 is the correct option.

n(A) = n(B) ⇒

1. A = B

2. A ≠ B

3. A contains all the elements of B and B contains all the elements of A.

4. none of these

Answer

n(A) = n(B) means A and B have the same number of elements, i.e. they are equivalent sets. The elements need not be the same, so A and B need not be equal, need not be unequal, and need not contain all the elements of each other. So, none of the given statements is necessarily true.

Hence, option 4 is the correct option.

Number of elements in { prime numbers between the integers 7 and 11 } is:

1. 0

2. 3

3. 5

4. 2

Answer

The integers between 7 and 11 are 8, 9 and 10. None of these is a prime number. So, the set has no element.

Hence, option 1 is the correct option.

If A = { 0, 1, 2, { }, {0} }, then n(A) is:

1. 5

2. 4

3. 3

4. 6

Answer

The elements of A are 0, 1, 2, { } and {0}, which are 5 distinct elements.

Hence, option 1 is the correct option.

N = { x : x is a natural number and x² ≤ 5 }, then set N is:

1. {-2, -1, 0, 1, 2}

2. {0, 1, 2}

3. {1, 2}

4. {-2, -1, 0}

Answer

The natural numbers are 1, 2, 3, ......

For x = 1, x² = 1 ≤ 5

For x = 2, x² = 4 ≤ 5

For x = 3, x² = 9 > 5

So, N = { 1, 2 }.

Hence, option 3 is the correct option.

W = { x is a whole number and x² ≤ 5 }, then set W is equal to:

1. {-2, -1, 0, 1, 2}

2. {0, 1, 2}

3. {1, 2}

4. {-2, -1, 0}

Answer

The whole numbers are 0, 1, 2, 3, ......

For x = 0, x² = 0 ≤ 5

For x = 1, x² = 1 ≤ 5

For x = 2, x² = 4 ≤ 5

For x = 3, x² = 9 > 5

So, W = { 0, 1, 2 }.

Hence, option 2 is the correct option.

I = { x is an integer and x² ≤ 5 }, then set I is equal to:

1. {-2, -1, 0, 1, 2}

2. {0, 1, 2}

3. {1, 2}

4. {-2, -1, 0}

Answer

The integers are ......, -2, -1, 0, 1, 2, ......

For x = 0, x² = 0 ≤ 5

For x = ±1, x² = 1 ≤ 5

For x = ±2, x² = 4 ≤ 5

For x = ±3, x² = 9 > 5

So, I = { -2, -1, 0, 1, 2 }.

Hence, option 1 is the correct option.

If A = { 1, 2, 3, 4, 5, ......... } and B = { 2, 4, 6, 10, 12 }, then sets A and B are:

1. disjoint

2. overlapping

3. finite

4. equivalent

Answer

A = { 1, 2, 3, 4, 5, ......... } is the set of natural numbers and B = { 2, 4, 6, 10, 12 }. The elements 2, 4, 6, 10 and 12 of B are all present in A, so the two sets have elements in common.

Hence, option 2 is the correct option.