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For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC Z, if {x € Z : x = 2 (mod 8)} CS and {r € Z:r = 2 (mod 12)} = S, then { € Z: x = 2 (mod 4)} C S. (b) For all SC Z, if {x € Z: x = 2 (mod 4)} CS, then {z € Z: x = 2 (mod 8)} CS and {r € Z: x= 2 (mod 12)} S.

For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC Z, if {x € Z : x = 2 (mod 8)} CS and {r € Z:r = 2 (mod 12)} = S, then { € Z: x = 2 (mod 4)} C S. (b) For all SC Z, if {x € Z: x = 2 (mod 4)} CS, then {z € Z: x = 2 (mod 8)} CS and {r € Z: x= 2 (mod 12)} S.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC Z, if {x € Z : x = 2 (mod 8)} CS and {r € Z:r = 2 (mod 12)} = S, then { € Z: x = 2 (mod 4)} C S. (b) For all SC Z, if {x € Z: x = 2 (mod 4)} CS, then {z € Z: x = 2 (mod 8)} CS and {r € Z: x= 2 (mod 12)} S.
Transcribed Image Text:For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC Z, if {x € Z : x = 2 (mod 8)} CS and {r € Z:r = 2 (mod 12)} = S, then { € Z: x = 2 (mod 4)} C S. (b) For all SC Z, if {x € Z: x = 2 (mod 4)} CS, then {z € Z: x = 2 (mod 8)} CS and {r € Z: x= 2 (mod 12)} S.
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