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Two sets A and B are said to be equivalent(≡) if each element of A is also an element of B and each element of B is also an element of A.
If elements are repetitive in one set, then it is not required for it to repeat in the other set for the two sets to be equivalent.
Examples ⇒
{ 1, 2, 3 } ≡ { 1, 3, 2}
{ 1, 2, 3 } ≡ { 1, 3, 2, 2, 1, 2, 3, 3 }
{ 1, 2, 3 } ≢ { 1, 3, 2, 2, 1, 2, 3, 3, 4 } Since 4 is not in first set
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De Morgan’s First Law The complement of the union of two sets is equal to the intersection of their complements i.e. (A ∪ B )' = A' ∩ B' De Morgan’s Second Law The complement of the intersection of two sets is equal to the union of their complements i.e. (A ∩ B )’ =...
A cartesian product between two sets is defined as the set consisting of all possible ordered pairs that can be formed by taking one element from each of the sets at a given time. If A and B are two sets such that a ∈ A and b ∈ B, then the cartesian product between A...
An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words, or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is...
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