Page 59 - Computer science 868 Class 12
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obj.day_to_date();
obj.display();
}
}
32. Using a truth table, state whether the following proposition is a Tautology, Contradiction or Contingency:
∼(P → Q) ↔ (∼P ∨ Q) [ISC 2019]
Ans.
P Q P → Q ∼(P → Q) ∼P ∼P ∨ Q
0 0 1 0 1 1
0 1 1 0 1 1
1 0 0 1 0 1
1 1 1 0 0 1
The final column has all 0's. Hence, it is a contradiction.
33. (a) Given the Boolean function F(A, B, C, D) = Σ(0, 2, 3, 4, 5, 8, 10, 11, 12, 13). [ISC 2019]
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
Ans. F(A, B, C, D) = Σ (0, 2, 3, 4, 5, 8, 10, 11, 12, 13)
CD
AB C'.D' C'.D C.D C.D'
0 1 3 2
A'.B' 1 0 1 1
4 5 7 6
A'.B 1 1 0 0
12 13 15 14
A.B 1 1 0 0
8 9 11 10
A.B' 1 0 1 1
Quad 1: (m +m +m +m ) = B'D'
0
8
10
2
Quad 2: (m +m +m +m ) = C'D'
0
8
12
4
Quad 3: (m +m +m +m ) = B'C
11
10
3
2
Hence, F(A, B, C, D) = B'D' + BC' + B'C
(b) Given the Boolean function F(P, Q, R, S) = π(0, 1, 2, 8, 9, 11, 13, 15). [ISC 2019]
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
Ans. R+S R+S' R'+S' R'+S
0 1 3 2
P+Q 0 0 0 0
4 5 7 6
P+Q' 1 1 1 1
12 13 15 14
P'+Q' 1 0 0 1
8 9 11 10
P'+Q 0 0 0 0
Quad 1: m .m .m .m = Q+R
0
1
8
9
Quad 2: (m .M .M .M ) = P'+S'
11
9
13
15
Pair 1: (m .m ) = P+Q+S
2
0
Hence, F(P, Q, R, S) = (Q + R).(P' + S').(P + Q + S)
34. The owner of a company pays the bonus to his salesmen as per the criteria are given below: [ISC 2019]
If the salesman works overtime for more than 4 hours but does not work on off days/ holidays.
OR
If the salesman works when festival sales are on and updates showroom arrangements.
OR
If the salesman works on an off day/holiday when the festival sales are on.
57
Boolean Algebra 57

