Help please it’s important-

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

Help i’ll give brainliest

andriy [413]

Answer:

(8, -2)

Step-by-step explanation:

It is reflected over the X axis

Because 8 is an x coordinate, it will not be changed. And because 2 is not an X coordinate it will be reversed, or turned to negative

4 0

2 years ago

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PLEASE HELP, ILL GIVE BRAINLIEST! SIMPLE MATHS.

dusya [7]

The answer is c i’m pretty sure

7 0

2 years ago

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HELP I WILL GIVEBRAINLIST! FALSE ANSWERS OR SPAM WILL BE REPORTED!!!!1

GuDViN [60]

Answer:

StartFraction 7 over 2 EndFraction can be used to find the unit rate if one divides 7 by 2 and compares the result to 1

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

we have the points

B(2, 7) and D(4, 14)

substitute the values

The unit rate is

therefore

StartFraction 7 over 2 EndFraction can be used to find the unit rate if one divides 7 by 2 and compares the result to 1

Step-by-step explanation:

8 0

2 years ago

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The length of a rectangle is twice the width. the perimeter is 32 cm more than the width. find the dimensions of the rectangle.

SCORPION-xisa [38]

Width: x
Length: 2x
Perimeter=2x+2x+x+x=6x
32 cm more than width means x+32
6x=x+32
5x=32
x=6.4
Dimension is 6.4×12.8 (width×length)

7 0

2 years ago