Assignment -1 Discrete Structures Rosen topic 1.1:
Question 6. a) True, because RAM B > RAM A > RAMC. b) True, because ROM C (-- removed HTML --) RESOLUTION B (F\/T) = T. c) False, because RESOLUTION A > RESOLUTION B (T/\T/\F) = F. d) False, because (T/\T) → F = F. e) False, because (F↔T) = F. Question 20. a) Exclusive or because both experiences are not required. b) Inclusive or because lunch can include both salad and soup. c) Exclusive or because both passport and voter registration card are not needed. d) Exclusive or because publish and perish can’t be done at same time. Question 24. a) If I will remember to send you the address, then you send me an e-mail message. b) If you were born in the United States, then you are a citizen …show more content…
Ans. 0.4 for “Fred and John are happy” and 0.2 for “Neither Fred nor John is happy?” Question 48. Yes because an assertion is a proposition. Question 49. a) Total statements are 100
If this nth statement is true then it should be not from those n but its number in list should be equal to n. The highest possible value is equal to 99. N = 99 The 99th statement is true and other are false. b) at least n statements means it can be n-1 the highest possible value is 51 1 to 50 are true are false 51 to 100 are true. c) No comment sorry. Rosen topic 1.2:
Question 4. ~s → (d → w) . Question 6. u → ((b32 /\ g1 /\ r1 /\ h16 ) \/ (b64 /\ g1 /\ r1 /\ h32)) . Question 10. P: Users can access the file system. q: The system software is being upgraded. r: Users can save new files.
Consistent because all specifications satisfied when p and r is true or q and r is true. Question 12. F: The file system is locked.
Q: The new messages will be queued.
S: The system is functioning …show more content…
b) p- Yoshiko knows Java. q- Yoshiko knows calculus. p/\q ~(p/\q)
Appling de morgan law ~(p/\q) = ~p\/~q
= ~p\/~q ans
Yoshiko don’t knows java or calculus.
c) p- James is young. q- James is strong. p/\q ~(p/\q)
Appling de morgan law ~(p/\q) = ~p\/~q
= ~p\/~q ans
James is not young or strong.
d)
p- Rita will move to Oregon . q- Rita will move to Washington. p\/q ~(p\/q)
Appling de morgan law ~(p\/q) = ~p/\~q
= ~p/\~q ans
Rita won’t move to Oregon and Washington. Question 12. a)
[¬p∧(p∨q)]→q
=(~p/\q)→q :. P will be opposite of negation p so value of p\/q depends on q
=~(~p/\q)\/q :. p → q ≡¬p∨q
=p\/~q\/q :.de morgan law
=T :.~q\/q is always true and p\/ T will also be true.
Hence proved that this statement is a tautology. b) [(p → q)∧(q → r)]→(p → r) = (~p\/q/\~q\/r) →(p→r) :. p → q ≡¬p∨q = (~p\/r)→(p→r) :.q/\~q is false and p\/F\/q = p\/q = (~p\/r)→(~p\/r) :. p → q ≡¬p∨q = T :. Two same truth values gives true in implication
Hence proved that this statement is a tautology. c) [p∧(p → q)]→q =q→q or F→q:. If p is true then this statement is dependent on q p∧(p
Question 6. a) True, because RAM B > RAM A > RAMC. b) True, because ROM C (-- removed HTML --) RESOLUTION B (F\/T) = T. c) False, because RESOLUTION A > RESOLUTION B (T/\T/\F) = F. d) False, because (T/\T) → F = F. e) False, because (F↔T) = F. Question 20. a) Exclusive or because both experiences are not required. b) Inclusive or because lunch can include both salad and soup. c) Exclusive or because both passport and voter registration card are not needed. d) Exclusive or because publish and perish can’t be done at same time. Question 24. a) If I will remember to send you the address, then you send me an e-mail message. b) If you were born in the United States, then you are a citizen …show more content…
Ans. 0.4 for “Fred and John are happy” and 0.2 for “Neither Fred nor John is happy?” Question 48. Yes because an assertion is a proposition. Question 49. a) Total statements are 100
If this nth statement is true then it should be not from those n but its number in list should be equal to n. The highest possible value is equal to 99. N = 99 The 99th statement is true and other are false. b) at least n statements means it can be n-1 the highest possible value is 51 1 to 50 are true are false 51 to 100 are true. c) No comment sorry. Rosen topic 1.2:
Question 4. ~s → (d → w) . Question 6. u → ((b32 /\ g1 /\ r1 /\ h16 ) \/ (b64 /\ g1 /\ r1 /\ h32)) . Question 10. P: Users can access the file system. q: The system software is being upgraded. r: Users can save new files.
Consistent because all specifications satisfied when p and r is true or q and r is true. Question 12. F: The file system is locked.
Q: The new messages will be queued.
S: The system is functioning …show more content…
b) p- Yoshiko knows Java. q- Yoshiko knows calculus. p/\q ~(p/\q)
Appling de morgan law ~(p/\q) = ~p\/~q
= ~p\/~q ans
Yoshiko don’t knows java or calculus.
c) p- James is young. q- James is strong. p/\q ~(p/\q)
Appling de morgan law ~(p/\q) = ~p\/~q
= ~p\/~q ans
James is not young or strong.
d)
p- Rita will move to Oregon . q- Rita will move to Washington. p\/q ~(p\/q)
Appling de morgan law ~(p\/q) = ~p/\~q
= ~p/\~q ans
Rita won’t move to Oregon and Washington. Question 12. a)
[¬p∧(p∨q)]→q
=(~p/\q)→q :. P will be opposite of negation p so value of p\/q depends on q
=~(~p/\q)\/q :. p → q ≡¬p∨q
=p\/~q\/q :.de morgan law
=T :.~q\/q is always true and p\/ T will also be true.
Hence proved that this statement is a tautology. b) [(p → q)∧(q → r)]→(p → r) = (~p\/q/\~q\/r) →(p→r) :. p → q ≡¬p∨q = (~p\/r)→(p→r) :.q/\~q is false and p\/F\/q = p\/q = (~p\/r)→(~p\/r) :. p → q ≡¬p∨q = T :. Two same truth values gives true in implication
Hence proved that this statement is a tautology. c) [p∧(p → q)]→q =q→q or F→q:. If p is true then this statement is dependent on q p∧(p