3. (10 points) Let R and S be relations on a set A. (a) Prove that if R and S are both symmetric, then $R \cap S$ is also symmetric.

          3. (10 points) Let R and S be relations on a set A.
(a) Prove that if R and S are both symmetric, then $R \cap S$ is also symmetric.

3. (10 points) Let R and S be relations on a set A.
(a) Prove that if R and S are both symmetric, then R ∩ S is also symmetric.

Added by Paul R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert James Kiss

Step 1

Since (x, y) is in R S, it means that there exists an element z in A such that (x, z) is in R and (z, y) is in S. Since R is symmetric, if (x, z) is in R, then (z, x) is also in R. Similarly, since S is symmetric, if (z, y) is in S, then (y, z) is also in Show more…

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