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Byju's Answer

Standard XII

Mathematics

Universal Set

Which of the ...

Question

Which of the following is not correct?

A \subseteq A^{C}

if and only if

A = ϕ

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A^{C} \subseteq A \Leftrightarrow A = x

where

x

is universal set

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A \cup B = A \cup C,

then

B = C

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A = C

is equivalent to

A \cup B = B \cup C

and

A \cap B = B \cap C

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Solution

The correct option is C If $A \cup B = A \cup C,$ then $B = C$

Let $A = {1, 2}$
$B = {2, 3, 4, 5}$
$C = {3, 4, 5}$
Here, $A \cup B = A \cup C$ But $B \neq C$

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Similar questions

If A = ${5, 6, 7, 8, 9}$ , B = ${x : 3 < x < 8 a n d x \in W}$ and C= ${x : x \leq 5 a n d x \in N}$ . Find:

(i) $A \cup B a n d (A \cup B) \cup C$

(ii) $B \cup C a n d A \cup (B \cup C)$

(iii) $A \cap B a n d (A \cup B) \cap C$

(iv) $B \cap C a n d A \cap (B \cap C)$

Is $(A \cup B) \cup$ C = A $\cup (B \cup C)$ ?

Is $(A \cap B) \cap C$ = A $\cap (B \cap C)$ ?

Q. If

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

is the universal set and

A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6}

verify the following.
(a)

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

(b)

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

(c)

(A^{'})^{'} = A

Q. If A = {a,b}, B = {b,c} and C = {b,c,d} ; then A

\times

\cup

C) = _____ .

(a) If A = {1, 3, 4, 8, 9, 12}, B = {1, 4, 9} and C = {2, 4, 8, 10}

Find (i) A ∪ (B ∩ C) (ii) A ∩ (B ∪ C) (iii) (A ∪ B) ∩ (A ∪ C) (iv) (A ∩ B) ∪ (A ∩ C)

(b) If A = (2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5, 6} and C = (1, 3, 5, 7, 9, 11, 13}

Verify (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(iii) (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) (iv) (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)

Y = {x : x is an even number less than 12}

Z = {x : x is an odd number less than 12}

Show that (i) union of sets of distributive over intersection of sets.

(ii) intersection of sets is distributive over union of sets.

Q. If

A, B

and

C

are three subsets of a non-empty set

X

, then

(A^{'} \cap B^{'} \cap C) \cup (B \cap C) \cup (A \cap C)

is equal to

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Which of the following is not correct?

The correct option is C If A∪B=A∪C, then B=C Let A={1,2} B={2,3,4,5} C={3,4,5} Here, A∪B=A∪C But B≠C

The correct option is C If $A \cup B = A \cup C,$ then $B = C$

Let $A = {1, 2}$
$B = {2, 3, 4, 5}$
$C = {3, 4, 5}$
Here, $A \cup B = A \cup C$ But $B \neq C$