1. (B-A) V (A Λ B) = B
2. (A + B) V (A Λ B) = A V B
help me to prove this.
please? thanx so much.
by 
ukodus
ANSWERS: 1
-
Note, your question uses combinations of symbols from different proof systems. The inverted-v sign is not usually found in the same line as a plus sign. Books disagree about what the signs mean. To prove your results using the principle of bivalence and truth tables, write the truth table and show it is always true, for every combination of truth for A and B: Write out the formula. Under that should be four rows. In row 1, A is T and B is T in row 2, A is T and B is F in row 3, A is F and B is T in row 4, A is F and B is F Write T/F under A and B according to each row. The first calculation is (A-B) Look up the value for - in the truth table for that logical connective for each row. Write it under the -. Continue this until you have the value for the whole expression under the '='. The final result should look something like this: (B.-.A)V(A.n.B)=.B. .T.F.T.T.T.T.T.T.T. .F.F.T.F.T.F.F.T.F. .T.T.F.T.F.F.T.T.T. .F.F.F.F.F.F.F.T.F. .b.c.a.e.a.d.b.f.b. The lower case letters show which order you fill in the columns c:b-a, d:a n b, e:c v b, f:e=b Since the value under the = is always T, (1) is proved.
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC