6.4 Truth Tables for Arguments

Brazil has a huge foreign debt. Therefore, either Brazil or Argentina has a huge foreign debt.

B//B v A T T T F valid

The disparity between rich and poor is increasing. Therefore, political control over economic equality will be achieved only if restructuring the economic system along socialist lines implies that political control over economic equality will be achieved.

D // P ⊃ (R⊃P) TT TT TF TT TT TT TF TT valid

If there are dried-up riverbeds on Mars, then water once flowed on the Martian surface. There are dried-up riverbeds on Mars. Therefore, water once flowed on the Martian surface.

D⊃W / D // W T F T T valid

~(G • M) / M v ~G // ~G

F T TF F T F FF F T F TT T T F TT T valid

K⊃~K // ~K

FF F TT T valid

P ≣ ~N // N v P

FF T TT T TF T FT F valid

K ≣ ~L / ~(L • ~K) // K⊃L

FF TFF T TT TFF F TF FTT T FT TFT T invalid

~(K ≣ S) / S ⊃ ~(R v K) // R v ~S

FT FFT TF FT FFT FF TF TFT TT TF TFT TT TF FFT TF TF TTF FF FT TFT TT FT TTF TT invalid

~A v R / ~(N • ~C) / R⊃C / C⊃~N // A v C

FT TFF TFF T FT FTT FTF T FT TFF TTT T FT TFT FTT T FF TFF TFF T FF FTT TTF T FF TFF TTT T FF TFT TTT T TT TFF TFF T TT FTT FTF F TT TFF TTT T TT TFT FTT F TT TFF TFF T TT FTT TTF F TT TFF TTT T TT TFT TTT F invalid

If fossil fuel combustion continues at its present rate, then a greenhouse effect will occur. If a greenhouse effect occurs, then world temperatures will rise. Therefore, if fossil fuel combustion continues at its present rate, then world temperatures will rise.

F⊃G / G⊃W // F⊃W T T T T F F F T T F T F T T T T F T T T T T T T valid

If microchips are made from diamond wafers, then computers will generate less heat. Computers will not generate less heat and microchips will be made from diamond wafers. Therefore, synthetic diamonds will be used for jewelry.

M⊃C / ~C • M // S T FF T FF F TT F TT T FF T FF T TF T TF valid

If national elections deteriorate into TV popularity contests, then smooth-talking morons will get elected. Therefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected.

N⊃S // ~N⊃~S T F T F F F T T T T F F T T T T invalid

Einstein won the Nobel Prize either for explaining the photoelectric effect or for the special theory of relativity. But he did win the Nobel Prize for explaining the photoelectric effect. Therefore, Einstein did not win the Nobel Prize for the special theory of relativity.

P v S / P // ~S T F T T T F F T invalid

If high school graduates are deficient in reading, they will not be able to compete in the modern world. If high school graduates are deficient in writing, they will not be able to compete in the modern world. Therefore, if high school graduates are deficient in reading, then they are deficient in writing.

R ⊃~C / W ⊃~C // R ⊃W FF FF T FF TF F TT TT T TT TT F TF FF T TF TF T TT TT T TT TT T invalid

R⊃R // R

T T invalid

C ≣ D / E v ~D // E⊃C

T TF T T FF T F TT T F TT T F TF F F FF T T TT F T TT T invalid

A⊃B / (A • B) ⊃ C / A ⊃ (C⊃D) // A⊃D

T TT TT T T TT FF F T TF TT T T TF TT F F FT TT T F FT FF F F FT TT T F FT TT F T FT TT T T FT TF T T FT TT T T FT TT T T FT TT T T FT TF T T FT TT T T FT TT T valid

S⊃T / S⊃~T / ~T⊃S // S v ~T

TFF FT TF FTT TT TT TTF FT FF TTT TF TT invalid

~(W • ~X) / ~(X • ~W) // X v W

TFF TFF T FTT TFF T TFF FTT T TFT TFT F invalid

Z // E ⊃ (Z ⊃ E)

TT TF TT TT valid

G⊃H / R≣G / ~H v G // R≣H

TT FT T TF FT F FT TT F FF TT T TF FF T TT FF F TF TT F TT TT T valid

A ≣ (B v C) / ~C v B // A⊃B

TT FT T TT TT T TT FF F FF TT F FT FT T FT TT T FT FF T TF TT T valid

A ⊃ (N v Q) / ~(N v ~A) // A ⊃ Q

TT FTF T TT FTF F TT TFF T FF TFF F TT FTT T TT FTT T TT FTT T TF FTT T valid

L⊃M / M⊃N / N⊃L // L v N

TT TT TF TT FT TT FT TT TT FT TF TF TT FT TT TF invalid

E ⊃ (F • G) / F ⊃ (G ⊃ H) // E ⊃ H

TT TT T TT FF F FF TT T FF TT F FF TT T FF TF F FF TT T FF TT F TT TT T TT FF T TF TT T TF TT T TF TT T TF TF T TF TT T TF TT T valid

W⊃X / X⊃W / X⊃Y / Y⊃X // W≣Y

TT TT T TT FT F FT TF T FT TT F TF TT F TF FT T TT TF F TT TT T valid

J ⊃ (K⊃L) / K ⊃ (J ⊃ L) // (J v K) ⊃ L

TT TT TT FF FF TF TT TT TT TT TF TF TT TT TT TF TT TF TT TT FT TT TT FT invalid

K ≣ (L v M) / L⊃M / M⊃K / K v L // K⊃L

TT TT TT TT FT TT TT TT TF FF TT TF FT TF TT FT FT TT FT TF FT TF TT FT invalid

Either the USS Arizona or the USS Missouri was not sunk in the attack on Pearl Harbor. Therefore, it is not the case that either the USS Arizona or the USS Missouri was sunk in the attack on Pearl Harbor.

~A v ~M // ~(A v M) F FF F T F TT F T T TF F T T TT T F invalid

If racial quotas are adopted for promoting employees, then qualified employees will be passed over; but if racial quotas are not adopted, then prior discrimination will go unaddressed. Either racial quotas will or will not be adopted for promoting employees. Therefore, either qualified employees will be passed over or prior discrimination will go unaddressed.

(R⊃Q) • (~R⊃P) / R v ~R // Q v P TTFT TF T TTFT TF T FFFT TF T FFFT TF F TTTT TT T TFTF TT T TTTT TT T TFTF TT F valid