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3 years ago

Determine the truth value of the statement when p is T, q is F, and r is F

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Given P is T, q is F and r is F.

Let us find p ↔ q first.

↔ is called bi-conditional operator and is true when p and q both are matched.

Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)

~p v r = ~T v F = F v F = F

Hence (p↔q)→(~pvr) = F → F = T (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)

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Write a conditional statement. Write the converse, inverse, and contrapositive for your statement and determine the truth value

MrRa [10]

Conditional statement is a statement with a hypotesis and a conclusion:

$If \text{ \underline{ hypothesis } } p, then \text{ \underline { conclusion } } q$

or mathematically $p\rightarrow q$ .

Converse statement of $p\rightarrow q$ is statement $q\rightarrow p$ .

If you negate (that means stick a "not" in front of) both the hypothesis and conclusion, you get the inverse:

$\neg p\rightarrow \neg q$ .

Finally, if you negate everything and flip p and q (taking the inverse of the converse) then you get the contrapositive:

$\neg q\rightarrow \neg p$ .

Example:

1. Conditional statement: If I am sleeping, then I have closed eyes. (true)

2. Converse statement: If I have closed eyes, then I'm sleeping. (not necessarily true)

3. Inverse statement: If I'm not sleeping, then I haven't closed eyes. (not necessarily true)

4. Contrapositive statement: If I haven't closed eyes, then I'm not sleeping. (true)

3 0

3 years ago

What is 36/100 added with 4/10

Ipatiy [6.2K]

Answer:

0.76 or 19/25

Step-by-step explanation:

Convert 4/10 so that it has a common denominator with 36/100.

4/10 x 10/10 = 40/100

Now that the denominator is the same, just add the top values.

40/100 + 36/100 = 76/100

We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.

5 0

3 years ago

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gregori [183]

12 broski done no ina bit g sfe my Erika

3 0

3 years ago

Read 2 more answers

Please help me with these

Alex Ar [27]

When we approach limits, we are finding values that are infinitesimally approaching this x-value. Essentially, we consider the approximate location that this root or limit appears. This is essential when it comes to taking Calculus, and finding the limit or rate of change of a function.

When we are attempting limits questions, there are several tests we attempt first.

1. Evaluate the limit by substituting the value of the x-value as it approaches the value (direct evaluation of a limit)
2. Rearrangement of the function, such that we can evaluate the limit.
3. (TRIGONOMETRIC PROPERTIES)
$\lim_{x \to 0} (\frac{sinx}{x}) = 1$
$\lim_{x \to 0} (\frac{tanx}{x}) = 1$
4. Using L'Hopital's Rule for indeterminate limits, such as 0/0, -infinity/infinity, or infinity/infinity.

For example:

1) $\lim_{x \to 0}\frac{\sqrt{x} - 5}{x - 25}$

We can do this using the first and second method.
<em>Method 1: Direct evaluation:</em>

Substitute x = 0 to the function.
$\frac{\sqrt{0} - 5}{0 - 25}$
$= \frac{-5}{-25}$
$= \frac{1}{5}$

<em>Method 2: Rearranging the function
</em>
We can see that x - 25 can be rewritten as: (√x - 5)(√x + 5)
By rewriting it in this form, the top will cancel with the bottom easily, and our limit comes out the same.

$\lim_{x \to 0}\frac{(\sqrt{x} - 5)}{(\sqrt{x} - 5)(\sqrt{x} + 5)}$
$= \lim_{x \to 0}\frac{1}{(\sqrt{x} + 5)}}$
$= \frac{1}{5}$

Every example works exactly the same way, and by remembering these criteria, every limit question should come out pretty naturally.

8 0

3 years ago

-4 + x / 2 = 3 urgent!

Zina [86]

$\frac{-4 + x}{2}$ = 3 Multiply both sides by 2
-4 + x = 6 Add 4 to both sides (to cancle out the -4)
x = 10

4 0

2 years ago