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What is the proof of transitivity in logic NOT with truth table if p is q and if r is s and either p or r is true therefore either q or s is true?
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.
Find an equation of joint variation if P varies jointly as q r and s One set of values is p equals 70 Q equals 7 R equals 5 and S equals 4?
If P varies directly with q, r and s then P = kqrs, where k is a constant. As 70 = k x 7 x 5 x 4 = 140k : k = 70/140 = 1/2 The equation of joint variation is P = ½qrs.
What is ths solution for P equals s r t solve for s?
P=s r t , so, s= P/(st)
P varies jointly as q r and s One set of values is p equals 70 q equals 7 r equals 5 and s equals 4 Find p when q equals 2 r equals 15 and s equals 7?
If P varies jointly as q, r and s - assume this is in direct proportion, then P ∝ qrs so P = kqrs where k is a constant.70 = k x 7 x 5 x 4 = 140k : k = 140/70 = 0.5When q = 2, r = 15 and s = 7 then,P = 0.5 x 2 x 15 x 7 = 105
What is the perimeter of a rectangle that you s 5 yd long and 3 yd wide?
well the formula is p=2(l+w) p stands for perimeter l stands for length w stands for width P= l+l+w+w =5+5+3+3 = 16
