Discuss the validity of the statement below. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If B = Ø, then ANB = Ø. Choose the correct answer below. O A. The statement is true because B is a subset of the intersection ANB. If B contains no elements, then ANB must contain no elements. O B. The statement is true because the intersection ANB is a subset of B. If B contains no elements, then AnB must contain no elements. OC. The statement is false because the intersection AnB is a subset of B. If A = {1} and B = Ø, then AnB = {1}. O D. The statement is false because B is a subset of the intersection ANB. If A = {1} and B = Ø, then AnB = {1}.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.2: Statements And Reasoning
Problem 56E: In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of...
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Discuss the validity of the statement below. Venn diagrams may be helpful. If the statement is true, explain why. If
not, give a counterexample.
If B = Ø, then ANB = Ø.
Choose the correct answer below.
O A. The statement is true because B is a subset of the intersection ANB.
If B contains no elements, then ANB must contain no elements.
O B. The statement is true because the intersection ANB is a subset of B.
If B contains no elements, then AnB must contain no elements.
OC. The statement is false because the intersection AnB is a subset of B. If A = {1} and B = Ø, then AnB = {1}.
O D. The statement is false because B is a subset of the intersection ANB. If A = {1} and B = Ø, then AnB = {1}.
Transcribed Image Text:Discuss the validity of the statement below. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If B = Ø, then ANB = Ø. Choose the correct answer below. O A. The statement is true because B is a subset of the intersection ANB. If B contains no elements, then ANB must contain no elements. O B. The statement is true because the intersection ANB is a subset of B. If B contains no elements, then AnB must contain no elements. OC. The statement is false because the intersection AnB is a subset of B. If A = {1} and B = Ø, then AnB = {1}. O D. The statement is false because B is a subset of the intersection ANB. If A = {1} and B = Ø, then AnB = {1}.
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