The contrapositive of -If x- A- B- then x- A or x- B- is

The correct option is D If x∉A and x∉B , then x∉A∪ B .Contrapositive of statement #34;If P then Q #34; is #34;If not Q then not P #34 ...

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Standard XII

Mathematics

Definition of Functions

The contrapos...

Question

The contrapositive of "If $x \in A \cup B$ , then $x \in A$ or $x \in B$ ", is

x \in A

x \in B

, then

x \in A \cup B

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x \notin A \cup B

, then

x \notin A

and

x \notin B

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x \notin A

and

x \notin B

, then

x \notin A \cup B

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x \notin A

and

x \notin B

, then

x \in A \cup B

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Solution

The correct option is D If $x \notin A$ and $x \notin B$ , then $x \notin A \cup B$ .
Contrapositive of statement "If P then Q" is "If not Q then not P"
Hence, C.

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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

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 $x \notin A .$

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. The inverse of "If

x \in A \cup B

, then

x \in A

x \in B

'', is

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

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The contrapositive of "If x∈A∪B, then x∈A or x∈B", is

The correct option is D If x∉A and x∉B, then x∉A∪B.Contrapositive of statement "If P then Q" is "If not Q then not P" Hence, C.

The contrapositive of "If $x \in A \cup B$ , then $x \in A$ or $x \in B$ ", is

The correct option is D If $x \notin A$ and $x \notin B$ , then $x \notin A \cup B$ .
Contrapositive of statement "If P then Q" is "If not Q then not P"
Hence, C.