Using propositional logic to prove that each argument is valid. If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Kraso was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewerly. Use letters J, L, C, T. So for this question, I am very confused and would appreciate any help offerd.

Step-by-step explanation:

We will first translate the situation to propositional logic. First, some notation is needed: is the or logical operation and is the symbol for logical implication. Define the following events:

J: Jose took the jewelry. L: Mrs Krasov lied, C: a crime was committed. T: Mr Krasov  was in town.

We will symbol the propositions in logical symbols. Recall that means negation

If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed:

Mr. Krasov was not in town:

If a crime was committed, then Mr. Krasov was in town:

We want to check if the conclusion Jose did not take the jewerly: can be deduced from the premises.

First, recall the following:

- if and a is true, then b is true.

- is logically equivalent to

Coming back to the problem, we have the following premises

where the equivalence for the logical implication was applied. REcall that the negation of an or  statement is g iven by

where is the and logical operator.

USing this, we get the premises

Since , by having , then it must be true that . Since , then it must be true that . This final conclusion implies that it is true that which is the statement that Jose did not take the jewelry.

if x decreases by 4 then y increases by 10

step-by-step explanation: