i need help with logic please

Reply Sun 20 Nov, 2011 11:52 am
1/The relation T on R (real numbers) is given by xTy iff x−y ∈ Q (rational numbers). Prove that T is an equivalence relation and find the equivalence class of 0 and √3.

2/ Let A be a non-empty set. Let P(A) denote the powerset of A. The relation R on
P(A) is given by BRC iff B ∩ C ̸= ∅ for B,C ∈ P(A). Prove or disprove that R is
an equivalence relation on P(A). If R is an equivalence Relation find the equivalence class if A = {0, 1, 2}
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Reply Tue 22 Nov, 2011 02:21 pm
1) Prove that it's reflexive, symmetric, and transitive.
2) Show that it's not transitive.
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