Questions On Arab Open University Of Computing Studies

727 Words Dec 6th, 2016 3 Pages
Arab Open University
Faculty of computing studies
Discrete Mathematics.
M131.
2016_2017.
TMA
Name: Mariam Ahmed Mostafa Abdelmnem Mohamed.
ID: 1551310073 Group : 4
I hereby declare that this submitted TMA work is a result of my own efforts and I have not plagiarized any other person 's work. I have provided all references of information that I have used and quoted in my TMA work.
Name of Student: Mariam Ahmed Mostafa Abdelmnem Mohamed.
Signature: Mariam Ahmed
Date: 6-12-2016
Question(1):

?
F F F
F T T
T F F
T T F
a)by using p , q , ¬ and ^ . P q ¬p ¬p ^ q
F F T F
F T T T
T F F F
T T F F

b)by using p , q , ¬ and V .
P Q ¬q P V ¬q ¬(p V ¬q)
F F T T F
F T F F T
T F T T F
T T F T F

c) by using p, q , ¬ and →.
P Q ¬p ¬q ¬p → ¬q ¬(¬p → ¬q)
F F T T T F
F T T F F T
T F F T T F
T T F F T F

Question(2): .
False.
Counter example : -1
(X +1)(X-2)=0 (0 +1)(0-2)>=0 -2≱0

.
True.
P(0)
(X +1)(X-2)< 0 True
P(3)
(X +1)(X-2)< 0 True.
P(3)
(X +1)(X-2)< 10}.
.|■(X)|=7
Reason: X={-3,-2,-1,0,1,2,3}

{x | xis natural number and 9x2 1 = 0}.
.|■(X)| = 0
Reason: 9x2-1=0 9x2=1 x2=1/9 x=±1/3 x = Ø

c)P(A), where A is the power set of {a, b, c}.
.|■(X)| = 8
Reason:|■(p(x))| = 2n = 23 = 8

d)A×B, where A={a, b, c} and B={1, 2, 3, 4, 5}.
.|■(A*B)| = 15
.Reason:|■(A*B)|=|■(A)|*|■(B)|
=3*5 = 15

e)ɸ ×B, where B={2, 4, 6,…

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