Difference of Two Sets

Q. If R is the set of real numbers and Q is the set of rational numbers, then what isR - Q?11.

Q.

If A = {1, 2, 3, 4}and B = {4, 5, 6, 7, 8}, then AUB = ?

1. {1, 2, 3, 4, 5, 6, 7, 8}

2. {1, 2, 3, 4, 4, 5, 6, 7, 8}

3. {1, 2, 5, 6, 7, 8}

4. {1, 2, 3, 5, 6, 7, 8}

Q.

Let A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}. Find A - B and B - A.

1. {1, 3, 5}; {8}

2. {1, 5}; {8}

3. {1, 3, 5}; {2, 4, 6}

4. {2, 4, 6}; {2, 4, 6}

Q.

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find :

(i) A - B (ii) A - C (iii) A - D

(iv) B - A (v) C - A (vi) D - A

(vii) B - C (viii) B - D (ix) C - B

(x) D - B (xi) C - D (xii) D - C

Q.

Write down all possible subsets of $A=\{1,\{2,3\}\}$.

Q. $\cap$If A and B are two disjoint sets, then $n\left(A\cup B\right)$ is equal to
(a) $n\left(A\right)+n\left(B\right)$
(b) $n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$
(c) $n\left(A\right)+n\left(B\right)+n\left(A\cap B\right)$
(d) $n\left(A\right)n\left(B\right)$
(e) $n\left(A\right)-n\left(B\right)$

Q. What is the difference between onto and into function?

Q. If two sets $A\&B$ are disjoint sets, then $n(A\cup B)=n\left(A\right)+n\left(B\right).$

1. False
2. True

Q.

Fill in the blanks to make each of the following a true statement :

(i) $A\cup A^{\prime }=........$ (ii) ${\Phi }^{\prime }\cap A=......$

(iii) $A\cap A^{\prime }=......$ (iv) $U^{\prime }\cap A=......$

Q. Is it true that for any sets A and $B,P\left(A\right)\cup P\left(B\right)=P\left(A\cup B\right)$? Justify your answer.

Q. Define a function as a set of ordered pairs.

Q. If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\},$ then

1. $A\cap B=(-2,-1)$
2. $B-A=R-(-2,5)$
3. $A-B=[-1,2)$
4. $A\cup B=R-(2,5)$

Q.

If A = {3, 6, 9, 12, 15, 18, 21}
B = {2, 4, 6, 8, 10, 12, 14, 16}
C = {5, 10, 15, 20}

$$\begin{array}{cc}A& B\\ 1.B-C& A.\{5,10,20\}\\ 2.A-C& B.\{3,9,15,21\}\\ 3.C-(A-B)& C.\{3,6,9,12,18,21\}\\ 4.C\cap (A-B)& D.\{15\}\\ & E.\{2,4,6,8,12,14,16\}\end{array}$$

1. 1 - E, 2 -C, 3 - D, 4 - A

2. 1 - E, 2 -C, 3 - A, 4 - D

3. 1 - C, 2 -A, 3 -E, 4 - D

4. 1 - C, 2 -A, 3 -D, 4 - E

Q. If E denote the complement or negation of an even E, what is the value of P(E) + P(E Bar?

Q.

1. {6, 8}

2. {7, 8, 9}

3. {3, 5, 6, 7, 8, 9}

4. {2, 4, 6, 8}

Q. Show that if A ⊂ B, then C – B ⊂ C – A.

Q. If A and B are two sets such that $n\left(A\right)=20,n\left(B\right)=25$ and $n\left(A\cup B\right)=40$, then write $n\left(A\cap B\right)$.

Q. In the following diagram, the shaded part represents

1. $(A-B{)}^C\cap (B-C)$
2. $(A-B)\cap (B-C{)}^C$
3. $(A-B{)}^C\cap (B-C{)}^C$
4. $(A-B)\cap (C-B)$

Q. Show that the following four conditions are equivalent:
(i) $A\subset B$ (ii) $A-B=\varphi$ (iii) $A\cup B=B$ (iv) $A\cap B=A$

Q. Let X be a non-empty set and let A, B, C be subsets of X. Consider the following statements : (1)A⊂C⇒(A∩B)⊂(C∩B), (A∪B)⊂(C∩B) (2)(A∪B)⊂(C∩B) for all sets B⇒A⊂C (3) (A∪B)⊂(C∪B) for all sets B⇒A⊂C Which of the above statements are correct ?

Q. 9. IfA-13, 6, 9, 12, 15, 18, 21), B 14, 8, 12, 16, 20 ), C= { 2, 4, 6, 8, 10, 12, 14, 16 }, D= {5, 10, 15, 20 }; find(G) A - B(v) C-A(vi) D(ix)A-C-AD-B(ii) A D iv) B-A(vii) B- C v) B D(ii)Vi1ViliC-B(x)

Q. Let A and B be two sets that $n\left(A\right)=16,n\left(B\right)=14,n\left(A\cup B\right)=25$. Then, $n\left(A\cap B\right)$ is equal to
(a) 30
(b) 50
(c) 5
(d) none of these

Q. Let $A=\{x:x^2-9\le 0,x\in Z\}$ and $B=\{x:|x-2|<3,x\in Z\}.$ Then the number of elements in $A\Delta B$ is

1. $3$
2. $4$
3. $5$
4. $6$

Q.

If A={2, 4, 6, 8, 10}
B={3, 4, 5, 6, 7}

So A-B=?

1. {2, 4, 5, 6, 7}

2. {2, 6, 8, 10}

3. {2, 8, 10}

4. {2, 3, 4, 5, 6, 7, 8, 10}

Q. Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R⁻¹ is

(a) {(3, 3), (3, 1), (5, 2)}
(b) {(1, 3), (2, 5), (3, 3)}
(c) {(1, 3), (5, 2)}
(d) None of these

Q.

If X and Y are two sets such that X ∪Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩Y have?

Q.

If A={1, 2, 3, 4, 5, 6}, B={1, 2}, then A-(A-B) is equal to

1. A

2. N

3. A$\cap$B

4. A$\cup$B

Q. If two sets $A$ and $B$ are such that $(A-B)=A$, then $A\cap B=$

1. $\varphi$
2. $A$
3. $B$
4. $A\cup B$

Q.

Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the number of elements in (A$\times$B) $\cap$ (B$\times$A) is

1. 18

2. 6

3. 4

4. 0

Q.

write the sets{ 1/3, 2/5, 3/7, 4/9} in the set builder form