Let A, B and C be sets such that phi ne A cap | vedclass

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(A) Given $\phi 
e A \cap B \subseteq C$. Check option $(A)$: If $(A - C) \subseteq B$ then $A \subseteq B$. Let $A = \{1, 2\}$,$B = \{2, 3\}$,$C = \

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If $(A - C) \subseteq B$ then $A \subseteq B$

Vedclass · Answer

(A) Given $\phi 
e A \cap B \subseteq C$. Check option $(A)$: If $(A - C) \subseteq B$ then $A \subseteq B$. Let $A = \{1, 2\}$,$B = \{2, 3\}$,$C = \{2\}$. Here $A \cap B = \{2\} \subseteq C$ and $A \cap B 
e \phi$. $A - C = \{1\}$. Since ${1} 
ot\subseteq \{2, 3\}$,the condition $(A - C) \subseteq B$ is not satisfied for this example. However,consider $A = \{1, 2\}$,$B = \{1, 3\}$,$C = \{2\}$. $A \cap B = \{1\} \subseteq C$ is false. Let $A = \{1, 2\}$,$B = \{2, 3\}$,$C = \{1, 2\}$. $A \cap B = \{2\} \subseteq C$. $A - C = \phi \subseteq B$ is true. But $A = \{1, 2\} 
ot\subseteq B = \{2, 3\}$. Thus,the statement in option $(A)$ is not true.

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

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