Logic: deductive validity Does Bob have a point, or is he confused? Explain your answer an essay of about 150 words. 6 For each argument, decide whether or not it is deductively valid. If it is not valid, briefly explain why. If it seems useful, describe a possible situation in which the premises are true, but the conclusion false. Example P1) P2)
Every Roman emperor before Constantine wae a pagan. Julian wae a Roman emperor.
C)
Julian was a pagan.
-A
a
b
c
d
e
Invalid. P 2 s a y s that Julian was a Roman emperor, but not that he ruled before Constantine. It would be possible for the premises to be true but the conclusion false, then, if Julian were a non-pagan Roman emperor after Constantine.
P1 )
Either Jane is in the kitchen, or Mary is in the kitchen.
P2)
Jane is not in the kitchen.
C)
Mary is in the kitchen.
P 1 ) Either inflation will increase, or personal debt will increase. P2) If the central bank does not increase interest rates, inflation will not increase. P3) The central bank will not increase interest rates. C)
Personal debt will increase.
P1 ) P2)
If the guerrillas have left the area, then there is traffic on the roads. There is no traffic on the roads.
C)
The guerrillas have not left the area.
P1 ) P2)
No member of the Green Party voted for the tax cut. Mr Jacobs did not vote for the tax cut.
C)
Mr Jacobs is a member of the Green Party.
P1 ) P2)
No member of the Green Party voted for the tax cut. Mr Jacobs voted for the tax cut.
C)
Mr Jacobs is not a member of the Green Party.
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