Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Prove |S U T| = |S| + |T| - |S ∩ T|?

Set theory

Prove |S U T| = |S| + |T| - |S ∩ T|

4 Answers

Relevance
  • asimov
    Lv 6
    1 decade ago
    Favorite Answer

    asumming |S| = a and

    |T| = b

    and

    |S ∩ T| = c

    if they have no common member then c=0

    if x belong to S U T it means

    case1) x belong to S only or

    case2) x belong to T only or

    case3) x belong to both

    case 1 is if x belong to S but not T, and the number of them are

    a-c

    case 2 : b-c

    case3 :c

    add all together

    a-c + b -c + c = a + b -c

  • 1 decade ago

    I am not sure what class this is, so the language might be different, but here would be my proof.:

    Assume that there exists a set S and a set T. By rule of Sets, the union of sets S and T is created by the items that are both unique to sets S and T as well as the items shared. The union is then comprised of the addition of sets S and T minus the intercetion, since the addition includes twice the shared items.

    Hope this helps you.

  • Draw venn diagrams. I'm not sure how you might go about it algebraically though, it seems pretty self evident as it is xD

    S U T is the set of all elements without repetition

    S + T is the set of all elements with repetition

    S ∩ T is the set of all elements which repeat.

    (the set of all elements with repetition) - (the set of all repetitions) = (the set of all elements without repetition).

  • Awms A
    Lv 7
    1 decade ago

    Two equations:

    |S U T| = |S| + |T \ S|

    |T| = |T \ S| + |S ∩ T|

    If you need to prove these, they're not hard.

    Then

    |T \ S| = |T| - |S ∩ T|

    so

    |S U T| = |S| + |T| - |S ∩ T|

Still have questions? Get your answers by asking now.