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Amanda [17]
3 years ago
12

5.12×4.001 ѕнσω уσυя ωσяк σℓz

Mathematics
1 answer:
GuDViN [60]3 years ago
6 0
I cant understand the wprds so no answer 4 uuuu
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Show that each of these conditional statements is a tautology by using truth tables. a) [¬p ∧ (p ∨ q)] → q b) [(p → q) ∧ (q → r)
nlexa [21]

Step-by-step explanation:

To show that a statement is a tautology using truth table - is to show that all the entries in the expression are truths T.

We can do this by taking each statement, expression by expression. For example, to show that

[~p ∧ (p ∨ q)] → q

is a tautology, knowing we have 3 columns, we have 2^3 = 8 rows. We start by putting putting truth values for p, q, and r respectively

Next, we find ~p, then find (p ∨ q), then find ~p ∧ (p ∨ q), before finally arriving at the required [~p ∧ (p ∨ q)] → q

TERMINOLOGIES AND SYMBOLS

- T means Truth

- F means False

- ~p means negation of p.

~p is F if p is T, and vice versa

- ∧ means conjunction.

p ∧ q is T only if p is T and q is T.

- ∨ means disjunction.

p ∨ q is T if either p or q is T.

- → is for conditional 'if then'

p → q is T if both p and q are T, or both p and q are F, or p is F and q is T, otherwise, it is F.

THE STEP BY STEP WORKINGS FOR THE STATEMENTS GIVEN ARE IN THE ATTACHMENT.

8 0
3 years ago
Read 2 more answers
If log 2 = a and log 5<br> b then<br> log<br> 32/125
sveta [45]

Answer:

log(32/125)

=log32 - log125 [log(x/y)=log(x) - log(y)]

=log(2)^2 - log(5)^3

=2log2-3log5 [log(x)^p=p log x]

=2a-3b

4 0
2 years ago
The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after
Olenka [21]
To solve this we are going to use the half life equation N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }
Where:
N_{0} is the initial sample
t is the time in years
t_{1/2} is the half life of the substance
N(t) is the remainder quantity after t years 

From the problem we know that:
N_{0} =100
t=200
t_{1/2} =1600

Lets replace those values in our equation to find N(t):
N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }
N(200)=100e^{( \frac{-138.6}{1600} )}
N(200)=100e^{-0.086625}
N(200)=91.7

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

8 0
3 years ago
3) The foot of a ladder is 1.2 m from a fence
VashaNatasha [74]

Answer: 4.5\ meters

Step-by-step explanation:

Using the data given in the exercise, we can draw the diagram attached, where "h" is the height of the building reached by the top of the ladder.

Notice that there are two similar triangles.

So, you can set up the following proportion:

\frac{1.8}{1.2}=\frac{h}{(1.2+1.8)}

Finally, in order to calculate the height on the building reached by the top of the ladder, you must solve for "h".

Therefore, the value of "h" is :

\frac{1.8}{1.2}=\frac{h}{3}\\\\(3)(\frac{1.8}{1.2})=h\\\\\frac{5.4}{1.2}=h\\\\h=4.5

5 0
3 years ago
What theorem can be used to prove that the two triangles are congruent?
Sergio [31]
SSS is my best answer.
4 0
2 years ago
Read 2 more answers
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