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Byju's Answer

Standard VII

Mathematics

Proper Subset

In each of th...

Question

In each of the following, determine whether the statements is true or false if it is true prove it if it false given an example.
If $x \in A$ and $A \subset̸ B$ then $x \in B$

True

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False

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Solution

The correct option is B False
Fro example let
A=(1,2),B={2,3,4,5}
Now 1∈A and A∈B but 1∈B

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Similar questions

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If x ∈ A and A ∈ B, then x ∈ B

(ii) If A ⊂ B and B ∈ C, then A ∈ C

(iii) If A ⊂ B and B ⊂ C, then A ⊂ C

(iv) If A ⊄ B and B ⊄ C, then A ⊄ C

(v) If x ∈ A and A ⊄ B, then x ∈ B

(vi) If A ⊂ B and x ∉ B, then x ∉ A

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
(i) If

x \in A

and

A \in B

, then

x \in B

(ii) If

A \subset B

and

B \in C

, then

A \in C

(iii) If

A \subset B

and

B \subset C

, then

A C

(iv) If

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v) If

x \in A

and

A \subset̸ B

, then

x \in B

(vi) If

A \subset B

and

x \notin B

, then

x \notin A

Q. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x ∈ A and A ∈ B, then x ∈ B (ii) If A ⊂ B and B ∈ C, then A ∈ C (iii) If A ⊂ B and B ⊂ C, then A ⊂ C (iv) If A ⊄ B and B ⊄ C, then A ⊄ C (v) If x ∈ A and A ⊄ B, then x ∈ B (vi) If A ⊂ B and x ∉ B, then x ∉ A

Q. Question 40

In the given question, state whether the given statement is True or False.

If a number a is divisible by b, then it must be divisible by each factor of b.

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If $x \in A$ and $A \in B$ then $x \in B$

(ii) If $A \subset B$ and $B \in C$ then $A \in C$

(iii) If $A \subset B$ and $B \subset C$ then $A \subset C$

(iv) If $A \subset̸ B$ and $B \subset̸ C$ then $A \subset̸ C$

(v) If $x \in A$ and $A \subset̸ B$ then $x \in B$

(vi) If $A \subset B$ and $x \notin B$ then $x \notin A .$

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In each of the following, determine whether the statements is true or false if it is true prove it if it false given an example.If x∈A and A⊄B then x∈B

The correct option is B FalseFro example letA=(1,2),B={2,3,4,5}A=(1,2),B={2,3,4,5}Now 1∈A1∈A and A∈BA∈B but 1∈B

In each of the following, determine whether the statements is true or false if it is true prove it if it false given an example.
If $x \in A$ and $A \subset̸ B$ then $x \in B$

The correct option is B False
Fro example let
A=(1,2),B={2,3,4,5}
Now 1∈A and A∈B but 1∈B