MATH1061: Discrete Mathematics - Truth Table - Mathematics Assignment Help

Assignment Task:

Answer all questions in the space provided. Show all

1. (a) Write down a truth table for the statement (p ! q) _ (? p ^ q), and circle the column that gives the final value. 

Is this statement a tautology, a contradiction, or neither?

(b) Show that the sentences p ! (q _ (? r ! p)) and q _ r are logically equivalent. 

There is a formula sheet on the last page of this exam which may help you, and if you choose to use these formulae then you must name the rule that you use at each step.

(c) Consider the following statements: 

(i) 8x 2 Q, 9y 2 Q such that x + y 2 Z; 

(ii) 9x 2 Q such that 8y 2 Q, x + y 2 Z. 

Determine whether each of the statements (i) and (ii) is true or false. You do not need to show your working.

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