Recall we define SXT = {(s, t): sS and t T}. For each of the following,...

 

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Recall we define SXT = {(s, t): sS and t€ T}. For each of the following, prove it if it is always true, else give a counterexample. • SXT=TXS • SXT = 0 if and only if S = 0 or T = 0 Sx (TxR) = (SxT) XR (SNT) XR=(SXR)n(TXR) • (S\T) XR=(SXR)\ (TxR) Recall we define SXT = {(s, t): sS and t€ T}. For each of the following, prove it if it is always true, else give a counterexample. • SXT=TXS • SXT = 0 if and only if S = 0 or T = 0 Sx (TxR) = (SxT) XR (SNT) XR=(SXR)n(TXR) • (S\T) XR=(SXR)\ (TxR)

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Answer To prove or disprove the statements lets define sets S T and R and examine each case separately 1 SXT TXS To prove this statement we need to show that for any sets S and T the set SXT is equal ... View the full answer