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Diffstat (limited to 'csci4511w/hw3.txt')
| -rw-r--r-- | csci4511w/hw3.txt | 91 |
1 files changed, 91 insertions, 0 deletions
diff --git a/csci4511w/hw3.txt b/csci4511w/hw3.txt new file mode 100644 index 0000000..88ee3a7 --- /dev/null +++ b/csci4511w/hw3.txt @@ -0,0 +1,91 @@ +1) + 1. Valid (it is always true) + 2. Neither (this is occasionally true) + 3. Neither + A⇒B (C) ~A⇒~B (D) C⇒D + T T T + F T T + T F F + T T T + + 4. Valid (A v ~A is always true) + 5. Neither + A B C A⇒B (D) B⇒C (E) D⇒E + T T T T T T + T T F T F F + T F T F T T + T F F F T T + F T T T T T + F T F T F F + F F T T T T + F F F T T T + 6. Valid + (A⇒B)⇒((~A|~C)⇒B) + A B C A⇒B (D) ((~A|~C)⇒B) (E) D⇒E + T T T T T T + T T F T T T + T F T F F T + T F F F T T + F T T T T T + F T F T T T + F F T T T T + F F F T T T + 7. Valid (at least one is always true) + A B A⇒B + T T T + T F F + F T T + F F T + 8. Neither + A B A^B (C) C∨~B + T T T T + T F F T + F T F F + F F F T + 9. Valid + A B C (P⇒Q)∧(Q⇒R) (D) D⇒(A⇒C) + T T T T T + T T F T T + T F T F T + T F F T T + F T T F T + F T F F T + F F T F T + F F F T T + 10. Valid (this truth table is really long) + +2) (A^B)⇒C == (~A∨~B)⇒C + 1. They are both true iff all 3 are true so no? + 2. Yes. This is the statement. + 3. No. AND and OR are not interchangable. + 4. No. + + 5. No. +3) + 1. ~~(~C∨~D)∨P + -> ~C∨~D∨P + 2. ~J∨(Wi^We) + -> (~J∨Wi) [a]^(~J∨We) [b] + 3. ~Wi∨D + 4. ~We∨C + 5. J + --REFUTATION-- + 6. ~P + 7. (1,6) ~C∨~D + 8. (7,3) ~Wi∨~C + 9. (8,4) ~Wi∨~We + 10. (9,2a) ~J∨~We + 11. (10,5) ~We + 12. (11,2b) ~J + 13. (5,12) NIL +4) + 1. A∨B∨C + 2. ~A∨B + 3. ~B [a]^ ~D [b] + 4. ~C∨D + --REFUTATION-- + 5. (1,4) A∨B∨D + 6. (3,5) A∨D + 7. (6,4) A + 8. (7,2) B + 9. (8,3) NIL
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