CSI Equivalences #40 Q6) (5 points) 1.4 Predicates and

CSI 2101AB, Winter 2018

Assignment 1 (5% of
final mark)

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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

 

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