Question

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6} and
C = {1, 2, 4, 6, 7}, then find
i) (AuB)uC
ii)(A-B)u(A-C)​

Answer 1

Step-by-step explanation:

we need to do union here.

means to collect numbers from both sets :-

(AUB)={1,2,3,4,5,6}

Now , according to question:-

i) (AUB)UC={1,2,3,4,5,6}U{1,2,3,4,6,7}

= {1,2,3,4,5,6,7}

ii) (A-B)U(A-C)={1,2}U{3}

={1,2,3}

Hope it helps you

Answer 2

Step-by-step explanation:

Given :-

A = {1, 2, 3, 4},

B = {3, 4, 5, 6},

C = {1, 2, 4, 6, 7}

To find :-

Find the following :

i) (AUB)UC

ii)(A-B)U(A-C)

Solution :-

Given sets are :

A = {1, 2, 3, 4},

B = {3, 4, 5, 6},

C = {1, 2, 4, 6, 7}

i) Finding (AUB)UC :-

AUB = {1, 2, 3, 4} U {3, 4, 5, 6}

=> AUB = {1,2,3,4,5,6}

Now,

(AUB)UC = {1,2,3,4,5,6} U {1, 2, 4, 6, 7}

=> (AUB)UC = { 1,2,3,4,5,6,7}

ii) Finding (A-B)U(A-C) :-

A-B = {1, 2, 3, 4} - {3, 4, 5, 6}

=> A-B = { 1,2}

and

A-C = {1, 2, 3, 4} - {1,2,4,6,7}

=> A-C = { 3}

Now,

(A-B)U(A-C) = { 1,2} U { 3}

=> (A-B)U(A-C) = { 1,2,3}

Answer:-

i) (AUB)UC = { 1,2,3,4,5,6,7}

ii) (A-B)U(A-C) = { 1,2,3}

Used formulae:-

→ If A and B are two non -empty sets then,

• The set of all elements in either A or in B or in both is called the Union of A and B .
• It is denoted by AUB
• The set of all elements in only A not in B is called the difference between A and B .
• It is denoted by A-B