1. Set - I
School of Science and Humanities
Subject : Higher Mathematics (CSE 501)
Course Teacher: N.Chandramowliswaran
M.Tech Information Technology[Networking]-2009
Batch: IT 2
Time: 1 Hour Max.Marks: 20
Answer all the following Questions 20 x 1 = 20 Marks
1. Say True or False ( ) ( ) ( )P Q P Q P Q P Q¬ ∨ ⇔ ¬ ∧ ∨ ¬ ∧ ¬ ∨ ∧
2. ( ) ( ) ( ) ( ) ( ) ( )P Q P R Q R P Q R P Q R P Q R ___?___∧ ∨ ¬ ∧ ∨ ∧ ⇔ ∧ ∧ ∨ ∧ ∧ ¬ ∨ ¬ ∧ ∧ ∨
a. ( )P Q R¬ ∧ ¬ ∧ b. ( )P Q R¬ ∧ ∧ ¬ c. ( )P Q R∧ ¬ ∧ ¬ d. ( )P Q R¬ ∧ ¬ ∧ ¬
3. ( ) ( ) ( )P P Q P Q ___?___ P Q∨ ¬ ∧ ⇔ ∧ ∨ ∨ ¬ ∧
a. ( )P Q¬ ∧ b. ( )P Q¬ ∨ c. ( )P Q∧ ¬ d. ( )P Q∨ ¬
4. Among the three statement formulae which of them forms a tautology.
(i) ( ) ( )Q P Q P Q∨ ∧ ¬ ∨ ¬ ∧ ¬
(ii) ( )Q P Q∧ ∨ ¬
(iii) ( )( )P P Q P→ ∧ →
a. (i) & (ii) b. (i) & (iii) c. (ii) & (iii) d. (i), (ii) , (iii)
5. Among the three statement formulae which of them forms a tautology.
I. P Q P Q∧ ⇒ ∧
II. ( ) ( )P P Q Q¬ ∧ ∨ ⇒
III. ( )P P Q Q∧ → ⇒
a. I & II b. I & III c. II & III d. I , II , III e. None of the above
6. Out of two statement formulae which of them forms a tautology.
I. ( ) ( ) ( )P Q R P R Q→ ⎯⎯→ ∨ → ∨⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
II. ( ) ( ) ( )P Q R P R Q→ ⎯⎯→ ∧ → ∧⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
a. I b. II c. I & II d. None of the above

2. 7. Among the three statement formulae which of them forms a tautology.
I. ( ) ( )Q P Q P¬ ∧ → ⇒ ¬
II. ( ) ( ) ( )P Q Q R P R→ ∧ → ⇒ →
III. ( ) ( ) ( )P Q P R Q R R∨ ∧ → ∧ → ⇒
a. All the above b. None of the above c. I & II d. II & III
8. Out of two statement formulae which of them forms a tautology.
I. ( ) ( ) ( )P Q R S P S Q S R→ → ⎯⎯→ ∨ → ∨ → ∨⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
II. ( ) ( ) ( )P Q R S P S Q S R→ → ⎯⎯→ ∧ → ∧ → ∧⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
a. I b. II c. I & II d. None of the above
9. Among the three statement formulae which of them forms a tautology.
I. ( ) ( ) ( ) ( )P Q R P S Q S R S S∨ ∨ ∧ → ∧ → ∧ → ⎯⎯→⎡ ⎤⎣ ⎦
II. ( ) ( ) ( ) ( )P Q Q R R S P S→ ∧ → ∧ → ⎯⎯→ →⎡ ⎤⎣ ⎦
III. ( ) ( )Q R R Q¬ → ⎯⎯→ ¬ →
a. All the above b. None of the above c. I & II d. II & III
10. Among the three statement formulae which of them forms a tautology.
I. ( ) ( )Q R S U U S R Q⎡ ⎤ ⎡ ⎤¬ → → → ⎯⎯→ ¬ → → →⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦
II. ( ) ( ) ( )P Q P P Q P Q⎡ ⎤¬ ∧ → → → ⎯⎯→ →⎡ ⎤⎣ ⎦⎣ ⎦
III. ( ) ( ) ( )P Q P P Q P Q⎡ ⎤→ ¬ → → → ⎯⎯→ →⎡ ⎤⎣ ⎦⎣ ⎦
a. All the above b. None of the above c. I & III d. II & III
11. 1. ( ) ( )e f b e = ?∧ ∨ ∧ 2. ( ) ( )( )a b a c ?∨ ∧ ∨ =
12. ( ) ( )a c e g f d c ?∨ ∨ ∨ ∧ ∧ ∧ =
I. does not exist II. d III. e IV. c
0
a b
c
b
e f
I
a
0 h
e
c
a b
d
f g

3. 13.
Fig 1 Fig 2 Fig 3 Fig 4
Choose the correct statement
I. Figure 1 has both greatest and least element
II. Figure 2 has greatest element
III. Figure 3 has neither greatest nor least element
IV. Figure 4 has greatest element
14.
Fig 1 Fig 2 Fig 3
Fig 4 Fig 5 Fig 6 Fig 7
Choose the correct answer.
I. Fig 1 and Fig 5 does not form a Lattice, rest all form a Lattice
II. Fig 2 and Fig 3 forms a distributive Lattice
III. Fig 6 and Fig 7 forms a Lattice but not distributive Lattice
IV. Fig 4 forms a distributive Lattice
a b
c
d
e
f
b
c
d
e
f
a
a
c
d e
f
b
g h
f
e
c
a
b
d
5
10
20
4
2
1
a
b
c
d
e f h
e
c
a b
d
f g
a
b
c d
e
a
b c d
e
d
a
b c
e
f g
a
b
c
d
e

4. 15. Let ( )L,≤ be a Lattice. Then for every a and b in L,
a. ∨a b= b if and onlf if ________
b. ∧a b= a if and onlf if ________
c. ∧a b= a if and onlf if ________
16. Let L be a Lattice. Then Which of the following statements are true.
I. ∨ ∧a a= a ,a a= a
II. ∨ ∨ ∧ ∧a b=b a ,a b=b a
III. ( ) ( ) ( ) ( )∨ ∨ ∨ ∨ ∧ ∧ ∧ ∧a b c = a b c ,a b c = a b c
IV. ( ) ( )∨ ∧ ∧ ∨a a b = a ,a a b = a
17. Choose the correct statement
Let L be a Lattice. Then for every a, b, and c in L ,
I. ≤ ≤ ∨ ≤a c and b c if and onlf if a b c
II. ≤ ≤ ≤ ∧c a and c b if and onlf if c a b
III. ≤ ≤ ∨ ≤ ∨ ∧ ≤ ∧If a b and c d ,then a c b d ,a c b d
18. Let be the set of all integers. Let the standard less than or equal to symbol , " "≤
be the given partial order.
Then I. x y _______∧ = II. x y _______∨ =
19. _______ follows logically from the premises
( ) ( )C D,(C D) H, H A B R S∨ ∨ → ¬ ¬ → ∧ ¬ → ∨
a. R S∨ ¬ b. R S¬ ∨ c. R S¬ ∨ ¬ d. R S∨
20. _______ is tautologically implied by ( ) ( ) ( )P Q P R Q S∨ ∧ → ∧ →
a. S R∨ b. S R¬ ∨ ¬ c. S R¬ ∨ d. S R∨ ¬