December 1999
MA214 : DISCRETE MATHEMATICS

QUESTION 3

Total Marks: 15 Marks

• Question 1
• Question 2
• Question 4
• Question 5
• Cover Page

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SUGGESTED SOLUTIONS
for Question 3

(i)Suppose n =1 (mod 3 ). By writing n =3 k +1,where k is an integer,show that =1 (mod 3 ).[2 marks ]

(ii)Suppose n =2 (mod 3 ).Calculate (mod 3 ).[2 marks ]

(iii)Use (i)and (ii) to prove the implication “if n is an integer not divisible by 3,then =1 (mod 3 )”.[3 marks ]

Show that [~p(p V q )] -> q is a tautology by constructing a truth table.

Using algebraic laws show that ~((~pq ) V (~p~q )) V (pq )= p