CSI 2101AB, Winter 2018

Assignment 1 (5% of

final mark)

Prof. WonSook Lee

Name: Vedant Dubey

Student ID: 7736159

34

· Release Jan 19, 2018 — Due to

9am, Jan 29, 2018

· No email submission is accepted.

Please submit either to the assignment box in SITE or to the Virtual Campus

Q1)

(5 points) 1.1 Propositional Logic

exercise #42

Q2)

(2 points) 1.1 Propositional Logic

exercise #46

Q3)

(3 points) 1.2 Applications of

Propositional Logic #12

Q4)

(2 points) 1.3 Propositional

Equivalences #36

Q5)

(1 point) 1.3 Propositional

Equivalences #40

Q6)

(5 points) 1.4 Predicates and

Quantifiers #32

Q7)

(4 points) 1.4 Predicates and

Quantifiers #42

Q8)

(2 points) 1.4 Predicates and

Quantifiers #46

Q9)

(5

points) 1.5 Nested Quantifiers #18

Q10)

(1

point) 1.5 Nested Quantifiers #34

Q11)

(4

points) 1.5 Nested Quantifiers #38

Answers:

1. 1.1

Propositional Logic exercise #42

a.

If x=1, then (1+2=3) is true, so x:=x+1 is

executed. Final value of x is 2.

b.

If x=1, then (x+1=3) is false and (2x+2=3) is

false, which makes ((x+1=3)OR(2x+2=3)) false, so x:=x+1 is not executed. Final

value of x is 1.

c.

If x=1, then (2x+3=5) is true and (3x+4=7) is

true, which makes ((2x+3=5) AND (3x+4=7)) true, so x:=x+1 is executed. Final

value of x is 2.

d.

If x=1, then (x+1=2) is true and (x+2=3) is true,

so ((x+1=2)XOR(x+2=3)) is false, so x:=x+1 is executed. Final value of x is 1.

e.

If x=1, then (xP(y).

d.

Let x represent routers, y represent the

throughput, z represent the proxy server, P(x) represent “x is functioning

normally”, Q(y) represent “y is between 100 kbps and 500 kbps”, and R(z)

represent “z is in diagnostic mode”. Then the given statement becomes (Q(y)?¬R(z))à?xP(x).

8. 1.4

Predicates and Quantifiers #46

9. 1.5

Nested Quantifiers #18

10. 1.5

Nested Quantifiers #34

11. 1.5

Nested Quantifiers #38