Disjoint Sets

Q.

Which of the following is not true?

1. Every relation from the set A to the set B is a function from the set A to the set B.

2. Every function from the set A to the set B is a relation from the set A to the set B

3. If f is a function from A to B and (a, b) Є f, then f(a) = b, where a is called the pre-image of b under f.

4. If f is a function from A to B and (a, b) Є f, then f(a) = b, where b is called the image of a under f.

Q.

Which of the following is not an empty set?

1. Set of common points of two parallel lines in a plane

2. Set of smallest whole number

3. {x : x is a multiple of 7, x < 7, x ϵ N}

4. {x : 6 + 2x > 5x + 3, ϵ N}

Q.

Which of the following pair of sets are not equal?

1. P = {x:x² – 2x – 3 = 0}, and Q = {x:Xϵ N and X < 3}

2. P = {15, 20, 25, 30, 35, 40} and Q = {x : x is a multiple of 5, 10 < x < 45}

3. P = The set of prime numbers between 10 and 20 and Q = {11, 13, 17, 19}

4. P = {1, 2, 3, 4} and Q = {x:x ϵ N and X < 5}

Q. Consider the following statements :
A number $a_1{a}_2{a}_3{a}_4{a}_5{a}_6$ is divisible by 11 if
1. $(a_1+a_3+a_5)-(a_2+a_4+a_6)=0$
2.$(a_2+a_4+a_6)-(a_1+a_3+a_5)=0$
Which of these statements is/are correct?

1. 1 alone
2. 2 alone
3. Both 1 and 2
4. Neither 1 nor 2

Q. Let A and B be two sets. Show that the sets A × B and B × A have elements in common iff the sets A and B have an elements in common.

Q. Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to

1. 25
2. 34
3. 42
4. 41