If A-1-2-3- B-2- 4-5 and C-4- 1- 9- then verify A- B- C-A- B - A- C-

Given A={1,2,3}, B={2, 4,5} and C={4, 1, 9}. Then, nbsp;A∪ (B∩ C)={1,2,3}∪ ({2,4,5}∩{4,1,9}) ={1,2,3} ∪{4} ={1,2,3,4}......(1) nbsp; nbsp; nbsp; nb ...

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Byju's Answer

Standard VIII

Mathematics

Difference of Two Sets

If A=1,2,3, B...

Question

If $A = {1, 2, 3}, B = {2, 4, 5}$ and $C = {4, 1, 9},$ then verify $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ .

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Solution

Given $A = {1, 2, 3}, B = {2, 4, 5}$ and $C = {4, 1, 9} .$
Then, $A \cup (B \cap C) = {1, 2, 3} \cup ({2, 4, 5} \cap {4, 1, 9})$
$= {1, 2, 3} \cup {4}$
$= {1, 2, 3, 4} .$ .....(1) (1 mark)
Also, $(A \cup B) \cap (A \cup C) = ({1, 2, 3} \cup {2, 4, 5}) \cap ({1, 2, 3} \cup {4, 1, 9})$
$= {1, 2, 3, 4, 5} \cap {1, 2, 3, 4, 9}$
$= {1, 2, 3, 4} .$ .....(2)

By (1) and (2)
$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ (1 mark)

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Similar questions

If A = {1, 2, 3}, B = {4} and C = {5}, then verify that :

(i) $A \times (B \cup C) = (A \times B) \cup (A \times C)$

(ii) $A \times (B \cap C) = (A \times B) \cap (A \times C)$

(iii) $A \times (B - C) = (A \times B) - (A \times C)$

Q. If

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

and

C = {4, 1, 9},

then

A \cup (B \cap C)

= ___.

Q. If

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

and

C = {4, 1, 9},

then

A \cap (B \cup C)

= ___.

Q. If

A = {1, 3, 5, 7, 9}, B = {1, 2, 3}

and

C = {2, 3, 4}

.Verify:

A - (B \cup C) = (A - B) \cap (A - C)

Q. If

A = {1, 2, 3}, B = {4}, C = {5},

then verify that:

A \times (B \cup C) = (A \times B) \cup (A \times C)

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If A={1,2,3}, B={2,4,5} and C={4,1,9}, then verify A∪(B∩C)=(A∪B)∩(A∪C).

If $A = {1, 2, 3}, B = {2, 4, 5}$ and $C = {4, 1, 9},$ then verify $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ .