SOLUTION: Prove this 1. F∨~I 2. I∨H 3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F

SOLUTION: Prove this 1. F∨~I 2. I∨H 3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F

Algebra.Com

Question 1208642: Prove this
1. F∨~I
2. I∨H
3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Here is one way to do the derivation. There may be other approaches.

Number	Statement	Line(s) Used	Reason
1	F v ~I
2	I v H
3	~(G <--> J) --> ~H
:.	[ (~G v ~J) & (G v J) ] --> F
4	~F --> ~I	1	Material Implication
5	~I --> H	2	Material Implication
6	~F --> H	4,5	Hypothetical Syllogism
7	~H --> F	6	Transposition
8	~(G <--> J) --> F	3,7	Hypothetical Syllogism
9	[ (~G v ~J) & (G v J) ] --> F	8	Material Equivalence

Here's a list of rules of inference and replacement

RELATED QUESTIONS
How would you prove this argument valid ? 1. A > H 2. G > S 3. ~ K > (A v G) 4. ~ K (answered by math_helper)

1. (G->J)->(G->Q) 2. J*~Q... (answered by jim_thompson5910)

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)

I need help annotating this proof because I really dont understand. 1. ~H ∨ F (answered by Edwin McCravy)

Can someone please explain this to me? I am completely lost! Thanks. U =... (answered by MathLover1)

Two step proof: 1. (H * I) > J 2. H 3. I / J (answered by Edwin McCravy)

What is the determinant of the matrix F and G F= 0 3 0 0 0 a 2 b c d (answered by ikleyn,math_tutor2020)

Prove a quadrilateral with vertices G(1,1),H(5,3),I(4,5),J(0,3) is a... (answered by Alan3354)