Question
g) Use the truth table to show that the proportion is a tautology
.
(4mks)
h) Prove that
is divisible by 3 .
i) Given that
find
i.
ii.
(4mks)
h) Prove that
i) Given that
i.
ii.
Ask by Mann Pearson. in Kenya
Dec 17,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) The proportion
is a tautology.
b) is divisible by 3.
c) i. ; ii.
.
b)
c) i.
Solution

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Extra Insights
Consider the truth table for the expression
. When
is true,
can either be true or false depending on
. The expression states that if
is true, then for the whole statement to remain true,
must also be true. Thus, in all possible scenarios, the expression holds true, confirming it’s indeed a tautology.
To prove that
is divisible by 3 for all natural numbers
, consider
modulo 3. For
,
; for
,
; and for
,
. Thus, in all cases,
is divisible by 3.