SOLUTION: 1. (G⊃J) ⊃ (H⊃Q) 2. J • ~Q /~H

Algebra.Com
Question 1156947: 1. (G⊃J) ⊃ (H⊃Q)
2. J • ~Q /~H

Answer by RBryant(14)   (Show Source): You can put this solution on YOUR website!

1. (G⊃J) ⊃ (H⊃Q)
2. J • ~Q / ~H
--------------------------------------------------
3. we derive J by using line(s) 2 AND using the rule of Simplification.
4. we derive J v ~G by using line(s) 3 AND using the rule of Addition.
5. we derive ~G v J by using line(s) 4 AND using the rule of Commutation.
6. we derive G ⊃ J by using line(s) 5 AND using the rule of Implication.
7. we derive H ⊃ Q by using line(s) 1, 6 AND using the rule of Modus ponens.
8. we derive ~Q • J by using line(s) 2 AND using the rule of Commutation.
9. we derive ~Q by using line(s) 8 AND using the rule of Simplification.
10. we derive ~H as promised (which is the conclusion) by using lines 7,9 AND using the rule of Modus tollens.
We have demonstrated that which was asked of us to prove (QED). Smile :)

RELATED QUESTIONS

1. (G->J)->(G->Q) 2. J*~Q... (answered by jim_thompson5910)
How would you prove this argument valid ? 1. A > H 2. G > S 3. ~ K > (A v G) 4. ~ K (answered by math_helper)
Trying to write the proof and am stuck. 1.H > J 2.~(J & H) /... (answered by math_helper)
Solve the two step proofs below: 1. ~C 2. A > B 3. B > C / ~A 1. D > E 2. F > G (answered by Edwin McCravy)
Solve: F/(G -> H) v (~G ->... (answered by solver91311)
2g(h-g) ———— gh-j g=4, h=6, j=8; k=12. My ans 16 (answered by josgarithmetic)
Determine the expression for {{{ (h * j) }}}. {{{ h(x) = sqrt (x^2-1) }}} {{{ j(x) =... (answered by Fombitz)
Two step proof: 1. (H v I) > J 2. H / J (answered by Edwin McCravy)
Two step proof: 1. (H * I) > J 2. H 3. I / J (answered by Edwin McCravy)