To prove: For all sets A and B, if B C A° then AN B = Ø. I must: Suppose that BC A and AN B+ Ø. Suppose that A“ C BorAN BØ. Suppose that BC Aª and ANB= Ø. Suppose that BC A orAN B = Ø. Suppose that AC C BorAN B = Ø. Suppose that A° C B and An B+ Ø. O Suppose that A C Band ANB= Ø. Suppose that B C A° or AN B+ Ø.
To prove: For all sets A and B, if B C A° then AN B = Ø. I must: Suppose that BC A and AN B+ Ø. Suppose that A“ C BorAN BØ. Suppose that BC Aª and ANB= Ø. Suppose that BC A orAN B = Ø. Suppose that AC C BorAN B = Ø. Suppose that A° C B and An B+ Ø. O Suppose that A C Band ANB= Ø. Suppose that B C A° or AN B+ Ø.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.2: Corresponding Parts Of Congruent Triangles
Problem 16E: Given: HJ bisects KHL HJKL In Exercise 15, you cam delete Step 5 and 6 and still prove that KL. What...
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Transcribed Image Text:To prove:
For all sets A and B, if B C A° then An B = Ø.
I must:
Suppose that BC A and A N B+ Ø.
Suppose that A¢ C BorAN B+ Ø.
O Suppose that BC A and ANB= Ø.
O Suppose that BC A orA NB= Ø.
Suppose that A C BorA NB = Ø.
O Suppose that A C Band ANB+ Ø.
Suppose that A° C Band A NB= Ø.
Suppose that BC A° or An B+ Ø.
Transcribed Image Text:9. De Morgan's Law
10. Absorption Law
11. Complements of U and Empty Set
12. Set Difference Law
Proof: Let A, B,C be any sets. Then:
by
LHS = (AU B) – (C – A)
= (AU B) - (Cn A°)
by
= (AUB)n (Cn A°)°
by
= (AU B)n (C°U (A°)*)
by
= (AU B)n (CUA)
by
= (AUB)n (AUC)
by
ΞAU (BnC)
by
= AU (B- C)
RHS
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