1. Demonstrate the validity of the following identities by means of truth tables: (5 pts each) a. DeMorgan’s theorm for three va
riables: (x+y+z)’ = x’y’z’ And (xyz)’ = x’+y’+z’ b. The distributive law: x+yz = (x+y)(x+z)
1 answer:
Answer:
All the three statements presented are indeed valid and satisfy the De Morgan's theorem.
Step-by-step explanation:
The truth tables are presented in the attached images.
a) The statement (X + Y + Z)' = (X'Y'Z') has its proof in the first image attached.
b) The statement (XYZ)' = (X' + Y' + Z') has its proof in the second image attached.
c) The statement (X + YZ) = (X + Y)(X + Z) has its proof in the third image attached.
You might be interested in
The two other prime factors are 3 and 11
Answer:
cos2t/cos²t
Step-by-step explanation:
Here the given trigonometric expression to us is ,
We can write the numerator as ,
Recall the identity ,
Using this we have ,
Again , as we know that ,
Therefore we can rewrite it as ,
Again using the first identity mentioned above ,
Or else we can also write it using ,
Therefore ,
And we are done !
Additional info :-
<em>D</em><em>e</em><em>r</em><em>i</em><em>v</em><em>a</em><em>t</em><em>i</em><em>o</em><em>n</em><em> </em><em>o</em><em>f</em><em> </em><em>c</em><em>o</em><em>s</em><em>²</em><em>x</em><em> </em><em>-</em><em> </em><em>s</em><em>i</em><em>n</em><em>²</em><em>x</em><em> </em><em>=</em><em> </em><em>c</em><em>o</em><em>s</em><em>2</em><em>x</em><em> </em><em>:</em><em>-</em>
We can rewrite cos 2x as ,
As we know that ,
So that ,
On simplifying,
Hence,