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    Cuemath
    https://www.cuemath.com › algebra › difference-of-sets

    Difference of Sets - Definition, Venn Diagram, Complement

    • Let's look at an example to understand how to find the difference of two sets A and B. 1. Consider the two sets A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7, 9} 2. To find the difference A - B of these two sets, strik… See more

    Order of Difference of Sets

    Similar to how 5 - 3 is not the same as 3 - 5, we also need to be careful about the order when we compute the difference of sets. The difference of sets is not commutativ… See more

    Cuemath
    Example of Difference of Sets by Venn Diagram

    Consider two sets C = { a, b, c, d, e } and D = { a, e, f, g }. Then 1. C - D = { ̶a̶, b, c, d, ̶e̶ } - { ̶a̶, ̶e̶ , f, g } = {b, c, d} 2. D - C = { ̶a̶, ̶e̶, f, g } - { ̶a̶, b, c, d, ̶e̶ } = {f, g} The complement of a set A i… See more

    Cuemath
    Example of Complement of A Set

    Consider the example of set A = {1, 2, 3} and U = {1, 2 ,3, 4, 6}, then the complement of A is, A' (or) Ac= { ̶ ̶1̶,̶ ̶2̶,̶ ̶3̶, 4, 6} - { ̶ ̶1̶,̶ ̶2̶,̶ ̶3̶} = {4, 6}.
    If the univer… See more

    Cuemath
    Properties of Complement of A Set

    The properties of the complement are as follows which directly follow from its definition. 1. A ∪ Ac= U 2. A ∩ Ac= ∅ Here, ∅ is the empty set. DeMorgan's laws are: 1. (A ∩ B)C = … See more

    Cuemath
    Example of Symmetric Difference of Sets

    Let us consider two sets A = {1, 2, 4, 5, 8} and B = {3, 5, 6, 8, 9}. Then to find the symmetric difference of A and B, 1. Step - 1: Find A - B. A - B = {1, 2, 4, ̶5̶, ̶8̶} - {3, ̶5̶, 6,̶8̶, 9} = {1, 2, 4… See more

    Cuemath

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