Let p be the proposition \"It is September\", q be the proposition \"It is cold

Question

Let p be the proposition "It is September", q be the proposition "It is cold outside", and r be the proposition "I am Canadian". Translate the following expressions into English. 1. 2. Translate the following English expressions into logical statements. You must explicitly state what the atomic propositions are (e.g, "Let p be proposition ..") and then show their logical relation. a. I like teaching but I don't like email b. If it is cold outside then I need to wear a coat. a. Either I was born in October or I was not born in October. b. You are a COMP1805 student if and only if I am your instructor. (Alt + A)

Explanation / Answer

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Answer1)
a. It is cold outside and I am Canadian.
b. if it is not September then it is cold outside.
c. if I am Canadian or it is September then it is cold outside.
d. It is September but I am Canadian.

Answer2)
Let p be the proposition "I like teaching" , q be the proposition "I like email"
a. p ~q

Let p be the proposition "It is cold outside" , q be the proposition "I need to wear a coat"
b. p->q

Let p be the proposition "I was born in October"
c. p V ~ p

Let p be the proposition "Ypu are a COMP1805 student" , q be the proposition "I an your instructor"
d. p<=>q

Solution3)
a. False because condition 6 < 1 is not satisfy. For and we should have all condition true.

b. False because no condition satisfies.

c. True because 9> 8 satisfy.

d. True because 9> 2 true then 9=32 is true.

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