Question

4. If U={x{XEN,x<10} and A={x{ XEN, 25XS6} then (A)
(a) {1,6,7,8,9)
(c) {2,3,4,5}
(b) {1,2,3,43
(d) {
​

Answer 1

Answer:

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11th

>Applied Mathematics

>Set theory

>Applications of set theory in real life

>If X = {1,2,3,4,5,6,7,8,9, ...

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If X={1,2,3,4,5,6,7,8,9,10} is the universal set andA={1,2,3,4},B={2,4,6,8},C={3,4,5,6} verify the following.

(a) A∪(B∪C)=(A∪B)∪C

(b)A∩(B∪C)=(A∩B)∪(A∩C)

(c) (A

′

)

′

=A

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Answer

Correct option is

D

All three a,b and c are true.

given

X={1,2,3,4,5,6,7,8,9,10},A={1,2,3,4},B={2,4,6,8},C={3,4,5,6}

now from the given data

A∪B={1,2,3,4,6,8},B∪C={2,3,4,5,6,8}

Now A∪(B∪C)={1,2,3,4,5,6,8}and(A∪B)∪C={1,2,3,4,5,6,8}

∴A∪(B∪C)=(A∪B)∪C={1,2,3,4,5,6,8}

A∩B={2,4},A∩C={3,4},B∪C={2,3,4,5,6,8}

Now A∩(B∪C)={2,3,4}and(A∩B)∪(A∩C)={2,3,4}

∴A∩(B∪C)=(A∩B)∪(A∩C)={2,3,4}

A

′

={5,6,7,8,9,10}

therefore (A

′

)

′

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

therefore all three a,b,c are true

Step-by-step explanation:

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