SETS: PROOFS Prove the following statements: 1. For every three sets A, B, C it holds that (A U B) \ C = (A \ C) U (B \ C). 2. For every three sets A, B, C it holds that A U (B N C) = (A U B) N (A U C). 3. De-Morgan's law for sets: For every three sets S, T ≤ X it holds that (SNT)c = SC U Tº. 4. For every three sets S, T ≤ X it holds that S T ➡ TCC SC 5. What is the number of subsets of [n]? Prove your answer by induction.

SETS: PROOFS Prove the following statements: 1. For every three sets A, B, C it holds that (A U B) \ C = (A \ C) U (B \ C). 2. For every three sets A, B, C it holds that A U (B N C) = (A U B) N (A U C). 3. De-Morgan's law for sets: For every three sets S, T ≤ X it holds that (SNT)c = SC U Tº. 4. For every three sets S, T ≤ X it holds that S T ➡ TCC SC 5. What is the number of subsets of [n]? Prove your answer by induction.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

|| Let A,B be sets. Prove that AAB = if and only if A= B
Essentials of DISCRETE MATHEMATICS
True or False? Explain
Prove that if X∩Y = X∩Z and X∪Y = X∪Z, then Y = Z for all sets X,Y, and Z. Discord Math Question.
(4) Let A, B, C be subsets of a universal set U. Determine if the following statements are true or false. If true, prove them. If false, find a counterexample. (a) An(B\C) = (A \ B) n (A \ C) (b) If Ac C BC, then AC B. (c) (ANB) UC = (AUC) n(BUC).
Let A={x,y,z,1} and let B= {1,2,4}. If a set U= (A x B) U (B x A), how many elements are there in U?
Prove any set A,B and C prove that:
[4 marks] Decide if the following statement and proof is correct partially correct or false. "If A, B and C are sets then AC B and B C0 mplies ACC O correct O partially correct. O false. Proof Let A = (1,2), B = {1,2,3) and C = {1,2,3,4) then A c B,Bc C and AS C O correct O partially correct. O false [2 marks] Define the relations S={(1,2).(2.3)(3.4).(2.2)}then SoS is E(1,2),(1,3).(2,1),.(2.4).(2,2).(2,3)} VECG1,2).(1,3),(2,4)} E(1,2),(1,3),(2,4),(2,3)}| REDMI NOTE 8 PRO Al QUAD CAMERA choices.
Let U be the universe and let A, B and C be subsets of U. Determine whether the following statements are true or false. {x € Z : x is divisible by 2} c {y € Z: y is divisible by 4} If A C Q, then A CR If C = {x E U :x ¢ B and x g A}, then C C A° n BC
Let S and T be two sets. If both S and T are countable, prove that S U T (the union of S and T) is countable.
4. Proving by Example. Let U = {x|0 < x < 10}, A = { x € U|x is odd), and B:= {re U x is even). (a) Using A and B show that De Morgan's Law is true. (b) Using A and B Show that the remark number 7 on the lecture on inter- sections of Set is true.
Q1. Let U = {x: x e Z, 3 < x < 15} be the universal set, A = {x: x e U and 2 < x – 3 < 6}, B = {x: x e U and x is a factor of 24} and C = { x: x e U and 2x² < 72}. а) List all the elements belong to sets U, A, B and C. b) Find An č. c) Find A Ð B.