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LenaWriter [7]
3 years ago
12

Use a truth table to verify the first De Morgan law (p ∧ q)’ ≡ p’ ∨ q’.

Mathematics
1 answer:
Nutka1998 [239]3 years ago
6 0

Answer:

(p ∧ q)’ ≡ p’ ∨ q’

Step-by-step explanation:

First, p and q have just four (4) possibilities, p∧q is true (t) when p and q are both t.

p ∧    q

t t t

t f f

f f t

f f f

next step is getting the opposite

(p∧q)'

    <em>f</em>

<em>     t</em>

<em>     t</em>

<em>     t</em>

Then we get p' V q', V is true (t) when the first or the second is true.

p' V  q'

f  <em>f</em>  f

f  <em>t</em>  t

t  <em>t</em>  f

t  <em>t</em>  t

Let's compare them, ≡ is true if the first is equal to the second one.

(p∧q)'   ≡     (p' V q')

    <em>f              f </em>

<em>     t              t</em>

<em>     t              t</em>

<em>     t              t</em>

Both are true, so

(p ∧ q)’ ≡ p’ ∨ q’

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irga5000 [103]
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You are going to make 5 assemblies, where each assembly requires the use of 1 Type A Bolt. You have a container of bolts that co
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Answer:

Step-by-step explanation:

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Each assembly requires the use of 1 Type A bolt.

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(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?

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3 years ago
Find the inverse function of <br><img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%209%20%2B%20%20%5Csqrt%7B4x%20-%204%7D%20" id=
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Answer:

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Step-by-step explanation:

we would like to find the inverse of the following function:

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to do so substitute y for f(x):

\displaystyle y= 9 +  \sqrt{4x - 4}

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\displaystyle x= 9 +  \sqrt{4y - 4}

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divide both sides by 4:

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substitute back:

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and we're done!

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