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3 years ago

14

Three points lie on the same straight line. If each point can act as an endpoint, how many distinct line segments can be formed

using the set of points

1 answer:

Ede4ka [16]3 years ago

4 0

6. It is the three point times the amount of that a line is. every line is has two points three times two equal 6

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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.

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3 years ago

Use the Pythagorean Theorem to find the distance from Anna's house to the tree house. A) 105 B) 141 C) 193 D) 89

Naily [24]

The answer will be b 105

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Create a set of data with 7 values that has a mean of 30, a median of 26, a range of 50, and an interquartile range of 36.

kotykmax [81]

5, 10, 23, 26, 45, 46, 55

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2 years ago

Find dy/dx for (y^2/x) = 18 by implicit differentiation

Natasha2012 [34]

9514 1404 393

Answer:

dy/dx = y/(2x)

Step-by-step explanation:

The product formula can be used, along with the power rule.

d(uv) = du·v +u·dv

__

d(y^2/x) = d(18)

2y·dy/x -y^2/x^2·dx = 0

2x·dy -y·dx = 0 . . . . . . . . multiply by x^2/y

dy/dx = y/(2x) . . . . . . . . add y·dx, divide by 2x·dx

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2 years ago

Which of the following is the endpoint of the altitude of a regular pyramid

larisa [96]

It’s either vertex or base

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