tautologies.....?

Question

I dont like Jazz ( F )
I like Jazz or I like Rap ( T )
I like rap ( ? )

please help...

and show the truth table please

Answer 1

Let "J" represent the proposition "I like Jazz."
Let "R" represent the proposition "I like Rap."
Let "J v R" represent the disjunction of J and R ("J or R").

Here's a truth table:
J R J v R
T T T
T F T
F T T
F F F

It's given that "I don't like Jazz" (so J is false), and "I like Jazz or I like Rap" (so J v R is true). The only row of the table where J is false and J v R is true is the third row. Thus, the third row must be the case, so R is true--that is, I like rap.

Answer 2

You like jazz, and it cannot be told from the statements whether you like rap or not.

I don't like Jazz(F) implies I like Jazz. This statement automatically implies "I like Jazz or I like Rap" is T. Which leaves the third statement without a definite answer.

The tautology is :
((A is true) AND ( A or B)) is T

Let A be "I do not like jazz. Let B be "I like Jazz", and C is "I like rap.

A B C (B or C)

F T T T
F T F T
T F T T
T F F F

But from the first statement, A is F, so look over to the right and notice (B or C) is true. Also If you say A is false, look over to the right, you cannot say whether C is T or F because you have the same result for both cases.

God bless you. Have a good night.

Answer 3

A tautology is a statement that is always true. I'm not sure how that relates to your problem?

In any case, if you had simply posted:

I don't like Jazz.
I like Jazz or I like Rap.
Therefore I like Rap.

This is a correct line of logic, and it's an example of a "dysjunctive syllogism". The second sentence says you either like Jazz or you like Rap or you like both. The first sentence says you don't like Rap, which eliminates 2 of the three possibilities in the second sentence. Therefore you can conclude that you like Rap.

I'm a little confused though about the letters.

You put an F beside I don't like Jazz. Does that mean you like Jazz? If so, then you can't arrive at any conclusion about whether or not you like Rap, because the second sentence would be true if you like Rap or if you don't.

So what is it you are trying to do?

Answer 4

i like rap and jazz sounds