Disjoint

Q.

If $AandB$ are subsets of a set $X$, then what is $\left[A\cap (X-B)\right]\cup B$ equal to?

1. $A\cup B$

2. $A\cap B$

3. $A$

4. $B$

Q.

State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = {n, m}, then $P\times Q=$ {(m, n), (n, m)}

(ii) If A and B are non-empty sets, then $A\times B$ is a non-empty set of ordered pairs (x, y) such that $xϵA$ and $yϵB.$

(iii) If A = {1, 2}, B = {3, 4}, then $A\times (B\cap \varphi )=\varphi$

Q. If \log2, \log(2^n-1) and \log(2^n+3) are in AP, then n =

Q. For any two sets, prove that:
(i) $A\cup \left(A\cap B\right)=A$
(ii) $A\cap \left(A\cup B\right)=A$

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)
4. n(A)+n(B)-n(A $\cap$ B)

Q.

If n(A) + n(B) + n(C) = n(AUBUC) then what are the sets A, B, C are called?

1. equal

2. equivalent

3. disjoint

4. joint

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

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.

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. 8. Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B ) 9. Using properties of sets, show that (i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A. 8 . Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B ) 9. Using properties of sets, show that (i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A.

Q. $(A-B)-(B-C)=$___

1. A - B
2. B - C
3. A - C
4. A - B - C

Q.

Using properties of sets show that

(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.

Q. If p, q, r are prime numbers such that p^2-q^2=r. Find all the possible ordered pairs.