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3 years ago

Can someone help me asap

Mathematics

1 answer:

kompoz [17]3 years ago

8 0

3x + 4y ≥ 90

hope it helps

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For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)

spayn [35]

Answer:

The statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

The statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

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:

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

$\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A)$ by the logical equivalence involving conditional statement.

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

$\equiv \lnot B \lor (\lnot A \land A)$ by Distributive law.

$\equiv \lnot B \lor (A \land \lnot A)$ 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:

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

$\equiv (\lnot P \lor \lnot P)\land P$ by the logical equivalence involving conditional statement.

$\equiv P \land (\lnot P \lor \lnot P)$ by the Commutative law.

$\equiv (P \land \lnot P) \lor (P \land \lnot P)$ 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.

8 0

3 years ago

Pls help me with this

nevsk [136]

Answer is C.

3x and 4x² are not like terms, as their exponents do not share the same power (3x has a power of 1, 4x² has a power of 2)

5 0

3 years ago

Population growth is: A) Logarithmic B) Linear C) Exponential Please help ASAP!!! :(

Monica [59]

For this case we have that by definition the growth of a population is a function of the form:

$f (x) = a (b) ^ x$

Where,

a: initial population
b: growth rate
x: number of years

We observe then that the function is of the exponential type.

Answer:

C) Exponential

6 0

3 years ago

Forty more than the product of 2 and a number is twelve. What is the number?

posledela

Answer:

Logically, the answer is either 12 or 42

3 0

3 years ago

Marcus changed jobs after college. His old salary was $48000 per year. Now his new salary is 37% more per year. What is his new

spayn [35]

Answer:

65,760

Step-by-step explanation:

move decimal over two places to make a percent a decimal so .37

then multiply that times the 48000 to get 17,760 and then add that to the original 48000 to get 65,760

8 0

3 years ago