Let A- B and C be sets such that - A - B - C- Then which of the following statements is not true -

Let A={1,2,3} B={2,3,4} C={1,2,3,5,6} Here, A∩ B={2,3}⊆ C we can clearly see that nbsp; A C=ϕ⊆ B But A⊈ B So, option (d) is false. Similarly, rest of th ...

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Byju's Answer

Standard XII

Mathematics

Subset and Superset

Let A, B and ...

Question

Let $A, B$ and $C$ be sets such that $ϕ \neq A \cap B \subseteq C$ . Then which of the following statements is not true ?

B \cap C \neq ϕ

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

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(A - B) \subseteq C,

then

A \subseteq C

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(A - C) \subseteq B,

then

A \subseteq B

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Solution

The correct option is D If $(A - C) \subseteq B,$ then $A \subseteq B$
Let $A = {1, 2, 3} B = {2, 3, 4} C = {1, 2, 3, 5, 6}$
Here, $A \cap B = {2, 3} \subseteq C$
we can clearly see that
$A - C = ϕ \subseteq B$
But $A ⊈ B$ So, option $(d)$ is false.
Similarly, rest of the options can be solved.

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Let A,B and C be sets such that ϕ≠A∩B⊆C. Then which of the following statements is not true ?

The correct option is D If (A−C)⊆B, then A⊆BLet A={1,2,3} B={2,3,4} C={1,2,3,5,6} Here, A∩B={2,3}⊆C we can clearly see that A−C=ϕ⊆B But A⊈B So, option (d) is false. Similarly, rest of the options can be solved.

Let $A, B$ and $C$ be sets such that $ϕ \neq A \cap B \subseteq C$ . Then which of the following statements is not true ?

The correct option is D If $(A - C) \subseteq B,$ then $A \subseteq B$
Let $A = {1, 2, 3} B = {2, 3, 4} C = {1, 2, 3, 5, 6}$
Here, $A \cap B = {2, 3} \subseteq C$
we can clearly see that
$A - C = ϕ \subseteq B$
But $A ⊈ B$ So, option $(d)$ is false.
Similarly, rest of the options can be solved.