Discrete Math
1
Which of the following are statements?
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.
1. John is not wealthy but he is healthy and wise.
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. (P0 ^Q0)_(P0 ^Q)_(P^Q0)
Assuming that the notation “P0” and “Q0” represent P’ and Q’, and that the underscore character is meant to signify disjunction, the expression can be rewritten as:
4
Justify each step in the proof sequence below for [A!(B_C)]^B0 ^C0 !A0
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.
(A!C)^(C!B0)^B!A0
