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Determine whether the ff. proof is valid: for all sets A, B, and C, if A C B and BC C then AC. "Proof: Suppose A, B, and C are any sets such that AC B and B C C. Since A C B, there is an element x such that x E A and x E B, and since BC C, there is an element x such that x E B and x E C. Hence there is an element x such that x E A and хECand so A C С" O Yes, it is valid Insufficient information to find the answer O Not valid O Maybe

Determine whether the ff. proof is valid: for all sets A, B, and C, if A C B and BC C then AC. "Proof: Suppose A, B, and C are any sets such that AC B and B C C. Since A C B, there is an element x such that x E A and x E B, and since BC C, there is an element x such that x E B and x E C. Hence there is an element x such that x E A and хECand so A C С" O Yes, it is valid Insufficient information to find the answer O Not valid O Maybe

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...
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Answer the 2 questions, will upvote if complete, short solution/explanation will do
pls do not reject. thanks

Determine whether the ff. proof is valid: for all sets A, B, and C, if A C B and BC C then AC. "Proof: Suppose A, B, and C are any sets such that AC B and BC C. Since A C B, there is an element x such that x E A and x E B, and since BCC, there is an element x such that xEB and x E C. Hence there is an element x such that x E A and xE C and so A C C." O Yes, it is valid O Insufficient information to find the answer O Not valid O Maybe
Transcribed Image Text:Determine whether the ff. proof is valid: for all sets A, B, and C, if A C B and BC C then AC. "Proof: Suppose A, B, and C are any sets such that AC B and BC C. Since A C B, there is an element x such that x E A and x E B, and since BCC, there is an element x such that xEB and x E C. Hence there is an element x such that x E A and xE C and so A C C." O Yes, it is valid O Insufficient information to find the answer O Not valid O Maybe
Given the following sets: A = {2, 3, 4}, B = {1, 5, 10}, C = {-1, 1, 2}, D = {2, 5, 10} What is the cardinality of (A \ (Bu C)) \ (A \ (B u D)) ? O 2 O 1 O 4
Transcribed Image Text:Given the following sets: A = {2, 3, 4}, B = {1, 5, 10}, C = {-1, 1, 2}, D = {2, 5, 10} What is the cardinality of (A \ (Bu C)) \ (A \ (B u D)) ? O 2 O 1 O 4
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