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Diffstat (limited to 'OLD/csci4511w/hw3.txt')
| -rw-r--r-- | OLD/csci4511w/hw3.txt | 94 |
1 files changed, 0 insertions, 94 deletions
diff --git a/OLD/csci4511w/hw3.txt b/OLD/csci4511w/hw3.txt deleted file mode 100644 index 37af197..0000000 --- a/OLD/csci4511w/hw3.txt +++ /dev/null @@ -1,94 +0,0 @@ -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 but it turns out to be a tautology) - -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. - "If the night is quiet, then both the dog sleeps and the house is warm" - 5. No. - "The dog does not sleep or the night is not quiet or the house is warm" - -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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