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Question # 1: Formulate The Symbolic Expression (

The document contains 7 questions regarding logic expressions and circuits. It provides the solutions and explanations for each question. Question 1 defines logical expressions in words. Question 2 analyzes the validity of an argument using a truth table. Question 3 determines the output of gates in a circuit. Question 4 evaluates if two logical expressions are equivalent using a truth table. Question 5 verifies a logical equivalence using laws of logic. Question 6 constructs an input/output table for a logical expression. Question 7 draws a circuit for another logical expression.

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162 views3 pages

Question # 1: Formulate The Symbolic Expression (

The document contains 7 questions regarding logic expressions and circuits. It provides the solutions and explanations for each question. Question 1 defines logical expressions in words. Question 2 analyzes the validity of an argument using a truth table. Question 3 determines the output of gates in a circuit. Question 4 evaluates if two logical expressions are equivalent using a truth table. Question 5 verifies a logical equivalence using laws of logic. Question 6 constructs an input/output table for a logical expression. Question 7 draws a circuit for another logical expression.

Uploaded by

John
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Question # 1: Formulate the symbolic expression ~ ( p  q)  r in words using

p =: Today is Holiday
q =: It is raining
r =: We should study.

Solution:

If it is not true that today is holiday or it is raining, then we should study.

Question # 2: Check the validity of the following argument form using truth table:

pq
pq
p
Solution:

p q pq pq p
F F T F F
F T T T F
T F F T T
T T T T T

Row 2 and 4 are critical rows, in second row conclusion is false so it is an invalid argument.

Question # 3: Write the output of each gate in the following circuit

Solution:
X Y Z X Y ~Z  X Y   ~ Z ~   X Y   ~ Z 
0 0 0 0 1 1 0
0 0 1 0 0 0 1
0 1 0 0 1 1 0
0 1 1 0 0 0 1
1 0 0 0 1 1 0
1 0 1 0 0 0 1
1 1 0 1 1 1 0
1 1 1 1 0 1 0

Question # 4: Construct a truth table to determine whether the following statement is logically
equivalent or not:
 p  q   r and p   q  r  .

Solution:

p q r pq  p  q  r qr p   q  r
F F F F F F F
F F T F T T F
F T F F F T F
F T T F T T F
T F F F F F F
T F T F T T T
T T F T T T T
T T T T T T T

Columns 5 and 7 tells that they are not equivalent

5: By using the laws of logic verify the following logical equivalence:


Question #
~ ((~ p  q )   ~ p  ~ q  )   p  q   p .

Solution:
~   ~ p  q    ~ p  ~ q     p  q   ~  ~ p   q ~ q     p  q  Distributive Law
~  ~ p  t    p  q  Negation Law
~  ~ p    p  q  Identity Law
 p   p  q Double Negation Law
p Absorption Law

Question # 6: Construct the input/output table for ( p v q)

Solution:

Inputs Output
p q ( p v q)  r ~ ( p v q)  s
1 1 1 0
1 0 1 0
0 1 1 0
0 0 0 1

Question # 7: Construct circuit for the Boolean expression (~ p  q) ~ r .


Solution:

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