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monitta
3 years ago
8

20 POINTS

Mathematics
1 answer:
Brut [27]3 years ago
5 0

Answer:

Substitute (x+4)2−16 ( x + 4 ) 2 - 16 for x2+8x x 2 + 8 x in the equation x2+y2+8x−6y=24 x 2 + y 2 + 8 x - 6 y = 24 . (x+4)2−16+y2−6y=24 ( x + 4 ) 2 - 16 + y 2 ...

Step-by-step explanation:

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Step-by-step explanation:

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If a dice is rolled 18 times, how many times is the number 2 expected to come up? *
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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
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