Find the perimeter and area of the figure pictured below.

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

2 years ago

Elimination using addition and subtraction. <br> -4x+4y=-20<br> -2x+4y=-2

goldfiish [28.3K]

I would subtract the 2nd from the first one

so -4x - -2x = -2x

4y - 4y = 0

-20 - -2 = -18

-2x = -18

now I would divide that by -2 to get the value for x

so no we have x = 9

now you just have to substitute that into one of the equations and simplify to get y

-2 X 9 + 4y = -2

-18 + 4y = -2

4y =16

y = 4

3 0

3 years ago

Read 2 more answers

Which is equivalent to sqrt 180x^11 after it has been simplified completely?

lorasvet [3.4K]

Answer:

180x^5.5

Step-by-step explanation:

6 0

2 years ago

in isosceles triangle the length of a leg is 17 cm, the vase is 16 cm. find the length of the altitude to the base

bogdanovich [222]

Answer:

15 cm

Step-by-step explanation:

The altitude is one leg of the right triangle formed by the altitude, half the base, and the triangle side. The Pythagorean theorem applies, so you have ...

... (17 cm)² = (altitude)² + (16 cm/2)²

... altitude = √(17² -8²) cm = √225 cm

... altitude = 15 cm

8 0

2 years ago

Based on the information marked in the diagram, AABC and ADEF must be

Studentka2010 [4]

Answer:

a

Step-by-step explanation:

answer

8 0

2 years ago