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3 years ago

Find the missing side

Mathematics

1 answer:

Anton [14]3 years ago

6 0

The Missing side of the right triangle is 10

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Use logical equivalences (not a truth table) to reduce p → (q − p) to a tautology t. In other words, you should transform p → (q

schepotkina [342]

Answer:

The statement $p\rightarrow (q\rightarrow p)$ is a tautology.

$p\rightarrow (q\rightarrow p)\equiv \lnot p\lor (q\rightarrow p) \equiv \lnot p\lor (\lnot q\lor p) \equiv (p\lor \lnot p) \lor \lnot q \equiv T \lor \lnot q \equiv T$

Step-by-step explanation:

We have the following statement:

$p\rightarrow (q\rightarrow p)$

To reduce the statement to a tautology we need to use the table of logical equivalences as follows:

$p\rightarrow (q\rightarrow p)\equiv$

$\equiv \lnot p\lor (q\rightarrow p)$ by the the logical equivalence involving conditional statement.

$\equiv \lnot p\lor (\lnot q\lor p)$ by the the logical equivalence involving conditional statement.

$\equiv (p\lor \lnot p) \lor \lnot q$ by the Associative law.

$\equiv T \lor \lnot q$ by the Negation law.

$\equiv T$ by the Domination law.

7 0

3 years ago

Stephanie needs to cover her yard with 4103/4ft2 of soil she has enough for 125 ft2 in one bag and 65 ft 2 in another bag how mu

Evgen [1.6K]

Answer:

Stephanie requires 835.75 square feet more amount of soil to cover her yard.

Step-by-step explanation:

Given:

Total square feet of yard she need to cover with soil = $\frac{4103}{4}\ ft^2$

$\frac{4103}{4}\ ft^2$ can be rewritten as 1025.75 square feet.

Total square feet of yard she need to cover with soil = $1025.75\ ft^2$

Amount of soil in one bag = $125\ ft^2$

Amount of soil in other bag = $65\ ft^2$

Total Amount of soil she has is equal to sum of Amount of soil in one bag and Amount of soil in other bag.

Framing the equation we get;

Total Amount of soil she has= $125+65 = 190\ ft^2$

Now We need to find the Amount of soil she required more to cover the yard.

Amount of soil she required more is equal to difference of Total Amount of soil she has and Total square feet of yard she need to cover with soil.

Framing the equation we get;

Amount of soil she required more = $1025.75-190= 835.75\ ft^2$