Answer Happy

Is the following statement true or false? If R is any symmetric relation on a set A, then R-1 is symmetric. The statement is --Select--- Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order. Since R is symmetric and y Rx, then x Ry. Then by definition of R-1, y R-1x. Since R is symmetric and x R y, then y Rx. Therefore, by definition of a symmetric relation, R-1 is symmetric, and so the statement is true. 1 Then by definition of R-1, x Ry. Then by definition of R-1, y Rx. Then by definition of R-1, xR-1 y. Therefore, by definition of a symmetric relation, R-1 is not symmetric, and so the statement is false. Proof: 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that XR-1 y. 2. -Select- 3. --Select- 4. -Select- 5. ---Select-