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krek1111 [17]
3 years ago
15

rob says all numbers have an even number of factors marcia says some numbers have an odd number who is correct

Mathematics
2 answers:
Dmitriy789 [7]3 years ago
7 0

Answer:

Marcia is correct.

Step-by-step explanation:

We are given that,

Rob states that 'all numbers have an even number of factors'.

Marcia states that 'some numbers have an odd number of factors'.

Let us consider the number 36. Now, it is given that,

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Since, the repeated factor is counted only once. So, the factors of 36 are given by 1, 2, 3, 4, 6, 9, 12, 18 and 36.

This gives us that 36 has 9 factors and so, it has odd number of factors.

Hence, Marcia is correct.

Hoochie [10]3 years ago
6 0
No rob is incorrect because 8+8 equals 16 9+9 also equals 18 so they odds and even could make an even product
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Answer:

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Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement (A\rightarrow \lnot B)\land (B\rightarrow A), you need to use the logic laws as follows:

(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv

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\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A) by the Commutative law.

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\equiv \lnot B \lor (A \land \lnot A) by the Commutative law.

\equiv \lnot B \lor F by the Negation law.

Therefore the statement (A\rightarrow \lnot B)\land (B\rightarrow A) is a contingency.

b) To classify the statement (P\rightarrow \lnot P)\land P, you need to use the logic laws as follows:

(P\rightarrow \lnot P)\land P \equiv

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\equiv (P \land \lnot P) \lor (P \land \lnot P) by Distributive law.

\equiv F \lor F \equiv F by the Negation law.

Therefore the statement (P\rightarrow \lnot P)\land P is a contradiction.

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