Symbolic Logic Questions

Translate into symbols: If not Q then not P.

• ~Q → ~P

• Q → P

• ~P → ~Q

• P → Q

Translate into symbols: It is not true that if R then S.

• ~R → S

• R ∧ ~S

• ~R → ~S

• ~(R → S)

Translate into symbols: It is not true that if not P then R.

• ~(~P → R)

• ~P ∧ R

• P → ~R

• ~P → R

Translate into symbols: If P then Q is not true, then R.

• ~P → Q → ~R

• P → ~Q → R

• ~(P → Q) → R

• (P → ~Q) → R

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

T → R

T

∴ R

• Modus Ponens

• Modus Tollens

• No valid conclusion

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

S → ∼Q

Q

∴ ∼S

• Modus Ponens

• Modus Tollens

• No valid conclusion

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

∼Q → R

∼Q

∴ R

• Modus Ponens

• Modus Tollens

• No valid conclusion

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

T → R

R

∴ T

• Modus Ponens

• Modus Tollens

• No valid conclusion

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

∼R → S

∼S

∴ R

• Modus Ponens

• Modus Tollens

• No valid conclusion

Identify each symbolic argument as Modus Ponens, Modus Tollens, or no valid conclusion:

∼P → (R → Q)

∼P

∴ R → Q

• Modus Ponens

• Modus Tollens

• No valid conclusion