Discret Structures Question about inference, premises and conlusions. For each o

Question

Discret Structures Question about inference, premises and conlusions.

For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. "If I play hockey, then I am sore the next day." "l use the whirlpool if I am sore." "I did not use the whirlpool." "lf I work, it is either sunny or partly sunny." "I worked last Monday or I worked last Friday." "It was not sunny on Tuesday." "It was not partly sunny on Friday." "AII insects have six legs." "Dragonflies are insects." "Spiders do not have six legs." "Spiders eat dragon-flies "Every student has an Internet account." "Homer does not have an Internet account." "Maggie has an Internet account." "All foods that are healthy to eat do not taste good." "Tofu is healthy to eat." "You only eat what tastes good." "You do not eat tofu." "Cheeseburgers are not healthy to eat." "I am either dreaming or hallucinating." "I am not dreaming." "If I am hallucinating, I see elephants running down the road."

Explanation / Answer

a)Conditions : If I play hockey, I am sore next day.

if i am sore, i use whirlpool.

Statement : i didnot use whirlpool.

Conclusion: i didnot use whirlpool. => i am not sore. => I didn't play yesterday.

b) Conditions :If I work, it is either sunny or partly sunny.

Statements: I worked last monday or last friday.

it was not sunny on tuesday

it was not partly sunny on friday.

Conclusion : I worked last monday or last friday. => it is either sunny or partly sunny on monday or friday.

it was not sunny on tuesday => (if it was not partly sunny, i didn't work on tuesday.) or (if it was partly sunny, i worked on tuesday.)

it was not partly sunny on friday. and I worked last monday or last friday. => it was sunny on last friday.

c) Conditions : All insects have six legs

dragonfly are insects

spiders do not have six legs

spiders eat dragonflies

conclusion : (All insects have six legs) and (spiders do not have six legs) => spiders are not insects.

(All insects have six legs) and (dragonfly are insects) => dragonflies have six legs.

(spiders eat dragonflies) and (spiders are not insects) => spiders eat insects.

d) Conditions : Every student has an internet account.

homer doesnot have internet account.

maggie has an internet account.

conclusion : (Every student has an internet account.) and (homer doesnot have internet account.) => homer is not a student.

(Every student has an internet account.) and (maggie has an internet account.) => maggie is a student.

e) Conditions :All food that are healthy do not taste good.

tofu is healthy to eat.

you only eat wat tastes good.

you do not eat tofu.

cheesburgers are not healthy to eat

Conclusion : (All food that are healthy do not taste good) and ( tofu is healthy to eat) => tofu does not tast good.

(you only eat wat tastes good.) and (tofu does not tast good.) => you do not eat tofu.

(cheesburgers are not healthy to eat) and (All food that are healthy do not taste good.) => (cheesburger taste good).

f)Conditions: I am either dreaming or hallucinating

I am not dreaming.

If I am hallucinating, i see elphants running down the road.

Conclusion: (I am either dreaming or hallucinating ) and ( If I am hallucinating, i see elphants running down the road.) and (I am not dreaming. ) => I am not seeing elephants running down the road.

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