Superior olives OF SET THEORY FUNDAMENTALS Review Problems Problem 16.1 B then A

Question

Superior olives OF SET THEORY FUNDAMENTALS Review Problems Problem 16.1 B then An CC BnC. Let A, B, and C be sets. Prove that if A Problem 16.2 Anc Bnc but A B. Find sets A, B, and C such th Problem 16.3 nc and A uc g BuC but Find sets A, B, and c such that Anc g B A B. Problem 16.4 then BC SAC. Let A and B be two sets. Prove that if ACB Problem 16.5 C then Au B g C. Let A, B, and C be sets. Prove that if A S Cand B Problem 16.6 et A, B, and C be sets. Show that A x (Buc) (A x B) U (A x C). roblem 16 oblem 16.8 s the number 0 in 0? Why? s 0 (0)? Why? s 0 10)? Why?

Explanation / Answer

Solution:

A= { a , b , c }

B= { c , d }

C = { a, b, c , d}

AB = {c}

BC = {c, d}

thus

AB BC

again

AC = { a , b, c ,d }

BC = { a , b, c ,d }

AUC BUC

thus above two given are satisfied

But A B

A = { a , b ,c }

B = { b, c}

16.4

if A B
then,
A B=A ... (1)
A B=B ... (2)
Thus

(A B) = A'B'

which is B' .from (2)
and

(A B)'=A' B'

which is = A' from (1)

thus

A'B' = B'

A' B' = A'

Thus from the reverse logic B' A'

Hence proved

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