CMSC150 Homework 5 | Complete Solution

CMSC150
Introduction to Discrete Math
Summer 2015
Homework 5

The total number of points is 10. Your total score will be divided by 10 to produce a score over 100. Show all work.
1
Which of the following are statements? 4 points (1 point each)
1. She is a mathematics major.
2. 128=26
3. All that glitters is not gold.
4. Sleep tight and don’t let the bedbugs bite.
2
Let A, B, and C be the following statements:
A: John is healthy
B: John is wealthy
C: John is wise
Use A, B, and C as defined above to translate the following statements into symbolic form.3 points (1 point each)
1. John is not wealthy but he is healthy and wise.
1
2. John is neither healthy, wealthy, nor wise.
3. John is wealthy, but he is not both healthy and wise.
3
Simplify the following proposition to 2 logic operations using the laws of the algebra of propositions. Write each step
on a separate line with the algebra law you used as a justification. Missing steps will be penalized. (1 point)
(P0 ^Q0)_(P0 ^Q)_(P^Q0)
4
Justify each step with a comment in the proof sequence below for [A!(B_C)]^B0 ^C0 !A0(1 point)
1. A!(B_C)
2. B’
3. C’
4. B0 ^C0
5. (B_C)0
6. A’
5
Prove using a proof sequence that the argument is valid (hint: the last A’ has to be inferred). Justify each step with a
comment. (1 point)
(A!C)^(C!B0)^B!A0