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5 A in a S P?

Updated: 4/28/2022
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16y ago

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5 acts in a Shakespearean play

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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.


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


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The problem as stated does not allow for a solution for the value of S, however, the problem can at least be somewhat simplified. If m = p/5, then p + m can also be written as p + p/5, which simplifies to 1.2p so S = 1.2p


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Here the sample space is(s)=10, =>mod(s)=10 a=be the event of getting exactly 5 boys =>mod(a)=5 b=be the event of getting exactly 5 girls =>mod(b)=5 thus, p(a)=mod(a)/mod(s)=5/10=1/2 p(b)=mod(b)/mod(s)=5/10=1/2 p(5 boys and 5 girls)=p(a)*p(b)=1/2*1/2=1/4


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