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Q: What is 11 p on a s t?

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P=s r t , so, s= P/(st)

Prove: [ P -> Q AND R -> S AND (P OR R) ] -> (Q OR S) -> NOT, --- 1. P -> Q ___ hypothesis 2. R -> S ___ hypothesis 3. P OR R ___ hypothesis 4. ~P OR Q ___ implication from hyp 1. 5. ~R OR S ___ implication from hyp 2 6. ~P OR Q OR S ___ addition to 4. 7. ~R OR Q OR S ___ addition to 5. 8. Let T == (Q OR S) ___ substitution 9. (~P OR T) AND (~R OR T) ___ Conjunction 6,7 10. T OR (~P AND ~R) ___ Distribution from 9 11. T OR ~(P OR R) ___ De Morgan's theorem 12. Let M == (P OR R) ___ substitution 13. (T OR ~M) AND M ___ conjunction 11, hyp 3 From there, you can use distribution to get (T AND M) OR (~M AND M). The contradiction goes away leaving you with T AND M, which can simplify to T.

Let write the data in an increasing order: p q r s t.Since the median is 14, then r = 14, and we have: p q 14 s t.Since the mode is 11, then p = q = 11.Since the range is 9, then t - p = 9, t - 11 = 9, and t = 20.So, we have: 11 11 14 s 20.Since the mean is 25, we have:(11 + 11 + 14 + s + 20)/5 = 25(56 + s)/5 = 25 multiply by 5 to both sides56 + s = 125 subtract 56 to both sidess = 69So the data set is: 11 11 14 69 20

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