Introduction to Mathematical Reasoning (MATH 1800 A) – Fall 2020
Midterm Examination (November 4)
Beginning of Examination: 11:35 a.m.
End of Examination: 12:15 p.m.
The work has to be submitted by 12:35 p.m.
Total: 15 marks.
1. [8 marks] Let P , Q and R be statements. Write the truth table for the statement
“(P ∧Q)⇒ (∼ R)”.
2. [3 marks] Let Ω be the universe of discourse. For any x ∈ Ω, let P (x) and Q(x) be statements.
Consider the statement
“∃x ∈ Ω , ( (∼ P (x)) ∧Q(x) )”.
Negate this statement, and simplify your answer.
3. [4 marks] Let m,n ∈ Z be integers that are both even. Show that m2 + n2 is also even.

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