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Standard XII

Mathematics

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If a then b a...

Question

If a then b and if b then c $⟹$ If a then c.

False

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True

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Solution

The correct option is B True

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Similar questions

Q. Let

A, B, C

and

D

be four non-empty sets. The contrapositive statement of "If

A \subseteq B

and

B \subseteq D

, then

A \subseteq C

" is :

State, Whether the following statements are true of false.

(i) If $a < b, t h e n a - c < b - c$

(ii) If $a > b, t h e n a + c > b + c$

(iii) If $a < b, t h e n a c > b c$

(iv) If $a > b, t h e n \frac{a}{c} < \frac{b}{c}$

(v) If $a - c > b - d; t h e n a + d > b + c$

(vi) If $a < b, a n d c > 0, t h e n a - c > b - c where a, b, c and are real numbers and c \neq 0.$

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

(i)

x \in A

and

A \in B

, then

x \in B

(i i)

A \subset B

and

B \in C

, then

A \in C

(i i i)

A \subset B

and

B \subset C

, then

A \subset C

(i v)

A \subset̸ B

and

B \subset̸ C

, then

A \subset̸ C

(v)

x \in A

and

A \subset̸ B

, then

x \in B

(v i)

A \subset B

and

x \notin B

, then

x \notin A

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If a then b and if b then c ⟹ If a then c.

The correct option is B True

If a then b and if b then c $⟹$ If a then c.