By using truth tables, prove that: a. -(p v q) = ~p ^ ~q b. pv (q ar) = (p V q) ^ (p V r) c. (p → q) = (p ^q) → (q ^ r) d. (p + q) = (p ^ q) V (~p ^~q) e. -(p AqAr) = ~p V ~q V ~r f. ~(p v q V r) = ~p ^ ~q ^ ~r

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.CT: Test
Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...
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do a,b,c if you kind you can do all
By using truth tables, prove that:
a. -(p v q) = ~p ^ ~q
b. pv (q Ar) = (p V q) ^ (p V r)
c. (p → q) = (p ^ q)
d. (p + q) = (p ^ q) v (~p ^ ~q)
e. -(p ^qAr) = ~p V ~q V ~r
f. -(p V q V r) = ~p ^ ~q ^ ~r
→ (q ^ r)
Transcribed Image Text:By using truth tables, prove that: a. -(p v q) = ~p ^ ~q b. pv (q Ar) = (p V q) ^ (p V r) c. (p → q) = (p ^ q) d. (p + q) = (p ^ q) v (~p ^ ~q) e. -(p ^qAr) = ~p V ~q V ~r f. -(p V q V r) = ~p ^ ~q ^ ~r → (q ^ r)
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