BITS College
Discrete Mathematics
Math 161
Assignment 2:Applications
By:
Due Date : July 13 , 2021
Workout each question.
1. Check the validity of the following arguments
(a) Hayder works hard. If Hayder works hard, then he is a dull boy. If Hayder is a dull boy, then he will
not get the job. therefore, Randy will not get the job.
(b) If it does not rain or if it is not foggy, then the sailing race will be held and the lifesaving demonstration
will go on. If the sailing race is held, then the trophy will be awarded. The trophy was not awarded.
Thus, it rained.
2. Check validity of the following arguments, using rules of inference.
(a) p ∨ q, q ⇒ r, (p ∧ s) ⇒ t, ¬r, ¬q ⇒ (u ∧ s) ` r
(b) p ⇒ q, r ∨ s, ¬s ⇒ ¬t, ¬q ∨ s, ¬s, (¬p ∧ r) ⇒ u, w ∨ t ` u ∧ w
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3. Consider the following circuit
(a) Construct the input/output table.
(b) Give the compound proposition that corresponds to the circuit.
4. Construct a circuit for the proposition p ∧ q) ∨ (¬p ∧ r).
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5. Consider the following table.
p
1
1
1
1
0
0
0
0
q
1
1
0
0
1
1
0
0
r
1
0
1
0
1
0
1
0
s
0
1
0
0
1
0
0
0
(a) Construct a compound proposition having the given table as its truth table
(b) Construct a circuit having the given table as its input/output table.
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6. An alarm system has three different control panels in three different locations. To enable the system,
switches in at least two of the panels must be in the on position. If fewer than two are in the on position,
the system is disabled. Design a circuit to control the switches.
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