4. For each of these sets of premises, what relevant...

4. 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. a. ‘‘If I play hockey, then I am sore the next day.’’ ‘‘I use the whirlpool if I am sore.’’ ‘‘I did not use the whirlpool.’’ b. ‘‘Every student has an Internet account.’’ ‘‘Homer does not have an Internet account.’’ ‘‘Maggie has an Internet account.’’ c. ‘‘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.’’

Transcript

00:01 In this question we have been given a set of premises.

00:04 What relevant conclusion can be drawn explain the rule of inference used to obtain each conclusion from the premises? so in the first question, what all premises we have been given? let me write that first.

00:18 So i will consider my h premise to be i play hockey.

00:27 Then another argument given to be i am sore.

00:30 And the next one at say w it is i use wopolu so these are the three things that we are having first of all i apply negation of w okay and i will call it as my premise then again s implies w i will consider this as my second premise then negation of s which i will get by applying modest tallen on premise 1 and 2 so this is 1 2 3 and in 4 i get h implies s this will be my new premise in 5th i get h implies w so this is nothing but the hypothetical syllogism which is being applied to part two and part three in the sixth one we get negation of it that means the modulus modest it is modest here okay modest tallen from this i'm getting from three and four or from one and five that means i did not play the hockey is a required conclusion now let's move to the next premises so let's see what is given in part b so in part b what is given every student has an internet account so and it is given that homer does not have an internet account mackie has an internet account so what does i mean every student has an internet account for that means for every x s of x implies i of x x represent the class of a student and this is the internet so for every x means every student has an internet account then we have the second statement homer does not have an internet account that means negation of i which is representing the homer who are not having the internet account.

03:09 Now maggie of internet account, maggie has also internet account, so it can be written as i of maggie, correct, i of maggie.

03:23 So we know that sx is nothing but it is the student and this is the internet command or we can see here it is my internet account rather you can say correct.

03:42 Account and this is domain for both is people so let me write here as well the domain here is the domain of the people so in the first argument will be for every x which is given to be s of x minus i of x this is what i will call as my first premise and then in the second equation i will got s of homomorphism to the internet account.

04:25 Okay, universal instantaneous from, so this is getting from universal instantiation instantiation from equation one.

04:44 Correct, universal instantiation from equation one.

04:47 Then in the step three, i get negation i of homomorphism.

04:54 So this i am getting by applying the modest tolerance in equation number two and equation number three.

05:07 Correct.

05:08 So the conclusion will be the homer is not a student.

05:16 So in this question this is my required conclusion which is homer is not a stew.

05:24 So in this part we are going to consider all good that are good food that are really healthy to eat do not taste why.

05:34 So do not taste good so that means what for every eggs which is healthy it is always not taste good.

05:45 So this is how we represent it.

05:47 Then tofu is healthy to eat.

05:50 So this will be represented by h of tofu...

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