Hello,

Question

Struggling to get my head around this.

So we have this statement.
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If it rains on Monday then mark will carry an umbrella on Monday.

It does not rain on Monday.

You deduce:
Mark does not carry an umbrella on Monday.

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So if we assume that P means it does not rain on Monday.

and Q means Mark doesn't carry an umbrella on Monday.

So we know P>Q and Q is true then its valid? but this doesnt seem right as P is the opposite of the opening suggestion in the statement.

Any help?

Answer 1

P => Q
says nothing about what happens if ~P.

Answer 2

deduction is incorrect

draw Venn diagram

we only know that the rainstorm is in the umbrella circle. He could easily carry the umbrella in a dry northwest breeze.

hypothesis:
If a cow, then a mammal

Converse:
If a mammal, then a cow
(false)

Inverse:
If not a cow, then not a mammal (false)

Contrapositive:
If not a mammal, then not a cow (true)