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21 October, 17:17

Which of the following statements are always true for any two sets A and B?

(a)

If A ⊆ B, then A ⊂ B.

(b)

If A ⊂ B, then A ⊆ B.

(c)

If A = B, then A ⊆ B.

(d)

If A = B, then A ⊂ B.

(e)

If A ⊂ B, then A ≠ B.

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Answers (2)
  1. 21 October, 17:32
    0
    If A ⊆ B, then A ⊂ B.

    If A = B, then A ⊆ B.

    If A = B, then A ⊂ B.

    Step-by-step explanation:

    In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.

    In option (a),

    If A ⊆ B

    ⇒ A ⊂ B or A = B

    Thus, If A ⊆ B, then A ⊂ B.

    Option a is true.

    (b) If A ⊂ B

    ⇒ A is the subset of B

    That is, all elements of A are also the element of B,

    But we can not say A = B

    Thus, option b is not true.

    (c) If A = B

    ⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A (Because every set is the subset of itself)

    ⇒ A ⊆ B.

    Option c is true.

    (d) If A = B,

    ⇒ A ⊂ B

    Option d is true.

    (e) If A ⊂ B,

    Then we can not say that,

    A = B or A ≠ B

    Thus, option e is not correct.
  2. 21 October, 19:56
    0
    If A ⊆ B, then A ⊂ B.

    If A = B, then A ⊆ B.

    If A = B, then A ⊂ B.

    Step-by-step explanation:

    In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.

    In option (a),

    If A ⊆ B

    ⇒ A ⊂ B or A = B

    Thus, If A ⊆ B, then A ⊂ B.

    Option a is true.

    (b) If A ⊂ B

    ⇒ A is the subset of B

    That is, all elements of A are also the element of B,

    But we can not say A = B

    Thus, option b is not true.

    (c) If A = B

    ⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A (Because every set is the subset of itself)

    ⇒ A ⊆ B.

    Option c is true.

    (d) If A = B,

    ⇒ A ⊂ B

    Option d is true.

    (e) If A ⊂ B,

    Then we can not say that,

    A = B or A ≠ B

    Thus, option e is not correct.
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