NVIT CSCI 235 Discrete Structures Midterm 1 Lectures 1-5 PRINT NAME 9. Even thou
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NVIT CSCI 235 Discrete Structures Midterm 1 Lectures 1-5 PRINT NAME 9. Even though it may seem logical, the negation of an implication may or may not be equivalent to another implication Determine by any method if these two implications, a. and b., are equivalent or not. a. "If the sun is shining, then I am not going to the ball game b. "If the sun is not shining, I am going to the ball game. . . 10a. Given a 1011 0011 b 0110 1010 show the bitwise operations for the following three AND OR Exclusive OR 106. If not mentioned, which OK is assumed, inclusive OR or Exclusive OR · 10c.Using p, q, show the truth tables for Inclusive OR and Exclusive OR 10d, what are De Morgan's Laws used for? · NYIT CSCI 235 Discrete Structures Midterm 1 Lectures 1- Page 5 of 6Explanation / Answer
let us assume the value of the two statements as follows:
a= sun is shining
b= i am going to ball game
now if you will convert the 1st statement in terms of a and b and it can be written as follows:
a-> ~b
the 2nd statement can be written as follows:
~a->b
now we can prove using truth table that thiese 2 statements are not same
a b a->~b ~a->b
0 0 1 0
0 1 1 1
1 0 1 1
1 1 0 1
as we can see all the results of the 2 expression are not same so we can say that that 2 statements are not same.
10 a)
in OR the result is true if any of the value is true
a= 10110011
b= 01101010
a OR b=11111011
in AND the result is true if both the values are true
a= 10110011
b= 01101010
a AND b=00100010
in exclusive OR the result is true if the result is true ODD number of times
a= 10110011
b= 01101010
a OR b= 11011001
10 b)
if not mentioned in OR we use inclusive oR generally
10 c)
p q p OR q p ex OR q
0 0 0 0
0 1 1 1
1 0 1 1
1 1 1 0
10 d)
demorgans law is used for splitting the equation when the complement need to be taken for the expression as follows:
(a+b)' = a'b'
(ab)' = a'+b'
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