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LuckyWell [14K]
3 years ago
8

Show algebraically(using laws) that: ¬(p∧q)∨ p ≡ TRUE In your answer make sure that you (1) Show your steps (2) Do not skip any

steps and (3) Justify each step with the name of the law being used.
Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

We start by applying De Morgan's law:

\neg (p \wedge q) \vee p \equiv [(\neg p) \vee (\neg q)] \vee p.

We now use the fact that the disjunction is commutative:

[(\neg p) \vee (\neg q)] \vee p \equiv p \vee [(\neg p) \vee (\neg q)].

We now use the fact that the disjunction is distributive:

p \vee [(\neg p) \vee (\neg q)] \equiv [p \vee (\neg p)] \vee (\neg q).

Using the law of excluded middle, we have p \vee (\neg p) \equiv \textrm{TRUE}, so that:

[p \vee (\neg p)] \vee (\neg q) \equiv \textrm{TRUE} \vee (\neg q).

We finally use the fact that TRUE is the absorbing element of the disjunction:

\textrm{TRUE} \vee (\neg q) \equiv \textrm{TRUE}.

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kotegsom [21]
<h3>Answer:  $130</h3>

=======================================================

Explanation:

I'm assuming the bank is using simple interest (instead of compound interest).

If so, then,

i = P*r*t

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The amount of interest is $130

In the formula above, I used

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  • r = 0.0325 = annual interest rate in decimal form
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