Can someone help me with this discrete math question? Please asap :(

[Sera]

1. The mechanic knew either the oil filter was clogged or the oil pump was defective. He just replaced the oil filter. If he has replaced the oil filter, then he knew the oil pump is defective. Therefore, he knew the oil pump is defective.

a. By representing the propositional variable appropriately, list down the hypothesis and conclusion into the mathematical form.
b. Determine the appropriate rules of inference to be used to deduct the hypotheses in order to get the conclusion.
c. By using the truth table, show that the conjunction of the listed hypotheses implies the conclusion (e.g., H1  H2  H3  C) is a tautology.

 

[Dr.Peterson]

We can help, but we need to know what help you need. We also need to see what form of symbolism and rules you are using, so we can try to match what you are being taught. (I've seen some rather different ways to teach this.)

So please show your attempt, and ask specific questions where you aren't sure. And if you can do nothing, show us an example of what you have learned (both symbolism and rules).

 

[Steven G]

Let A be that he replaced the oil filter and B be he knew the oil pump was bad.

You given that he replaced the oil filter, meaning that you are given that A is true.
You are then told if he replaced the oil filter then he knew the oil pump was defective. This means A implies B


So this is what we have:

A
A implies B
What what do you think the conclusion is?