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Q. 4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(VII) B $\cup$ C $\cup$ D

Here,B = {3, 4, 5, 6},          C = {5, 6, 7, 8 } and           D = { 7, 8, 9, 10 } The union can be written as   B  C  D = {3,4,5,6,7,8,9,10}

Q.4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(VI) A $\cup$ B $\cup$ D

Here, A = {1, 2, 3, 4}, B = {3, 4, 5, 6} D = { 7, 8, 9, 10 } The union can be written as A  B  D = {1,2,3,4,5,6,7,8,9,10}

Q. 4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(V) A $\cup$ B $\cup$ C

Here, A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } The union can be written as  A  B  C = {1,2,3,4,5,6,7,8}

Q.4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(iv) B $\cup$ D

Here, B = {3, 4, 5, 6} D = { 7, 8, 9, 10 } B  D = {3,4,5,6,7,8,9,10}

Q. 4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(iii)  B $\cup$

Here,  B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } The union of the given sets are B  C = { 3,4,5,6,7,8}

Q.4 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(ii) A $\cup$ C

Here, A = {1, 2, 3, 4} C = {5, 6, 7, 8 } The union can be written as follows A  C = {1,2,3,4,5,6,7,8}

Q. 4 . If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find

(i) A $\cup$ B

Here, A = {1, 2, 3, 4}  B = {3, 4, 5, 6} The union of the set can be written as follows  A  B = {1,2,3,4,5,6}

Q.3 . If A and B are two sets such that A $\subset$ B, then what is A $\cup$ B ?

If A is subset of B then A  B will be set B.

Q.2 Let A = { a, b }, B = {a, b, c}. Is A $\subset$ B ? What is A $\cup$ B ?

Here, We can see elements of A lie in set B. Hence, A  B. And, A  B = {a,b,c} = B

Q.1  Find the union of each of the following pairs of sets :

(v).    A = {1, 2, 3}                     B = $\phi$

Here, A union B is A  B. A  B = {1,2,3}

Q.1 Find the union of each of the following pairs of sets :

(iv)  A = {x : x is a natural number and 1 $<$ x $\leq$6 }

B = {x : x is a natural number and 6 $<$ x $<$10 }

Here, A = {2,3,4,5,6} B = {7,8,9} A  B = {2,3,4,5,6,7,8,9} or it can be written as A  B = {x : x is a natural number and 1 x 10 }

Q.1 Find the union of each of the following pairs of sets :

(iii)   A = {x : x is a natural number and multiple of 3}                       B = {x : x is a natural number less than 6}

Here , A = {3,6,9,12,15,18,............} B = {1,2,3,4,5,6} Union of A and B is A  B. A  B = {1,2,3,4,5,6,9,12,15........}

Q.1 . Find the union of each of the following pairs of sets :

(ii)   A = [ a, e, i, o, u}          B = {a, b, c}

Union of A and B is A  B = {a,b,c,e,i,o,u}.

Q.1 Find the union of each of the following pairs of sets :

(i) X = {1, 3, 5}                                           Y = {1, 2, 3}

Union of X and Y is X  Y = {1,2,3,5}

Q12. State whether each of the following statement is true or false. Justify your answer.

(iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

Here, { 2, 6, 10 } and { 3, 7, 11} { 2, 6, 10 }   { 3, 7, 11} =  Hence,these are disjoint sets. So,statement is true.

Q12. State whether each of the following statement is true or false. Justify your answer.

(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

Here,  { 2, 6, 10, 14 }         and         { 3, 7, 11, 15} { 2, 6, 10, 14 }   { 3, 7, 11, 15} =  Hence, these are disjoint sets. So,given statement is true.

Q12. State whether each of the following statement is true or false. Justify your answer.

(ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets

Here,     { a, e, i, o, u } and { a, b, c, d } { a, e, i, o, u }  { a, b, c, d } = {a} Hence,these are not disjoint sets. So, statement is false.

Q12. 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.

Here,  { 2, 3, 4, 5 } and { 3, 6} { 2, 3, 4, 5 }  { 3, 6} = {3} Hence,these are not disjoint sets.  So,false.

Q11. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

R = set of real numbers. Q = set of rational numbers. R - Q = set of irrartional numbers.

Q10. If X= { a, b, c, d } and Y = { f, b, d, g}, find

(i) X – Y

(ii) Y – X

(iii) X $\cap$ Y

X= { a, b, c, d }                and              Y = { f, b, d, g} (i) X – Y = {a,c} (ii) Y – X = {f,g} (iii) X  Y = {b,d}
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