Disjoint

Q.

The condition for 2 sets A and B to be disjoint is

1. A ∩ B = ∅

2. A ∪ B = ∅

3. A - B = ∅

4. B - A = ∅

Q.

Which of the following pairs of sets are disjoint?

1. {3, 4, 5, 6, 7} and {x: x is a natural number and 7≤ x ≤ 10}

2. {x: x is an odd number} and {x: x is an even number}

3. {x: x is a prime number} and {x: x is an even number}

4. {x: x is an odd number} and {x:x is a multiple of 3}

Q. If A and B are not disjoint sets, then $n(A\cup B)$is equal to

1. n(A)+n(B)
2. n(A)+n(B)-n(A $\cap$ B)
3. n(A)+n(B)+n(A $\cap$ B)
4. n(A)-n(B)
5. n(A) n(B)

Q. If A and B are disjoint, then $n(A\cup B)$ is equal to

1. n(A)+n(B)
2. n(A).n(B)
3. n(A)
4. n(B)

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

Q. Which of the following pairs is/are a disjoint set(s)?

1. A = {x : x is an even prime number}
   B = {x : x is an even number less than 10}
2. C = {x : x is a solution of $x^2-25=0$ }
   D = {x : x is an integer such that x < 5}
3. E = {x : x is a whole number and a multiple of 7 less than 20}
   F = {x : x is a natural number and a multiple of 3}
4. G = {x : x is a natural number}
   H = {x : x is not a positive integer}

Q. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq XandY\cap Z$ is empty is:

1. $5^2$
2. $3^5$
3. $5^3$
4. $2^5$

Q.

If A and B are sets, then prove that A - B, $A\cap B$ and B- A are pair wise disjoint.

Q. 8.Which of the following pairs of sets are disjointG) 1, 2, 3, 4) and (x:x is a natural number and 4 3xs6)(i) a, e, i, o, u and c, d, e, f )(iii) Ix:x is an even integer ) and {x: x is an odd integer)

Q. 12. State whether each of the following statement is true or false. Justify your answer(i) {2, 3, 4, 5 ] and 3, 6) are disjoint sets.(ii) t a, e, i, o, u | and { a, b, c, d jare disjoint sets(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.(iv) 2, 6, 10 ) and 3, 7, 11] are disjoint sets