TEAM 2

Team – 2

1.   Identify  the Primitive statements in the following.

a)   In 2003 George W. Bush was the president of the United States.

è   Primitive statement (has true/false value).

b)  X+3 is a positive integer.

è   Non primitive statement

(statement doesn’t have truth/false value- It is open statement).

c)   Fifteen is an even number.

è   Primitive statement (has true/false value).

d)  If Jennifer is late for the party, then her cousin Zachary will be quite angry.

è   Non primitive statement (doesn’t have true/false value).

e)   What time is it?

è   Non Primitive statement

f)    As of June 30,2003, Christine Marie Evert had won the French open  a record seven times.

è   Primitive statement (has true/false value).

2.   Verify the first Absorption Law by means of a truth table.

·       pv(p^q) <=> p

P	q	p^q	pv(p^q)
1	1	1	1
1	0	0	1
0	1	0	0
0	0	0	0

·       p^(pvq) <=> p

p	q	pvq	P^(pvq)
1	1	1	1
1	0	1	1
0	1	1	0
0	0	0	0

Column  1^st & 4^th in both the cases are same, hence the absorption laws    pv(p^q)óp    &    p^(pvq)óp      are verified.

2.   Use truth tables to verify that each of the following is a                                                                 logical implication.

      I.                   [(p->q)^(q->r)] -> (p->r)

   II.                   [(p->q)^~q] -> ~p

III.                   [(pvq)^~p] -> q

IV.                   [(p->r)^(q->r)] -> [(pvq)->r]

a)       [(p->q)^(q->r)] -> (p->r)

p	q	r	p->q [A]	q->r [B]	A^B [C]	p->r [D]	C->D
1	1	1	1	1	1	1	1
1	1	0	1	0	0	0	1
1	0	1	0	1	0	1	1
1	0	0	0	1	0	0	1
0	1	1	1	1	1	1	1
0	1	0	1	0	0	1	1
0	0	1	1	1	1	1	1
0	0	0	1	1	1	1	1

               

                  

b)       [(p->q)^~q] -> ~p

p	q	p->q [X]	~q	X^~q [Y]	~p	Y->~p
1	1	1	0	0	0	1
1	0	0	1	0	0	1
0	1	1	0	0	1	1
0	0	1	1	1	1	1

c)             [(pvq)^~p] -> q

p	q	pvq   [X]	~p	X^~p [Y]	Y->q
1	1	1	0	0	1
1	0	1	0	0	1
0	1	1	1	1	1
0	0	0	1	0	1

 

             

  d)          [(p->r)^(q->r)] -> [(pvq)->r]

p	q	r	p->r [A]	q->r [B]	A^B [C]	pvq [D]	D->r [E]	C->E
1	1	1	1	1	1	1	1	1
1	1	0	0	0	0	1	0	1
1	0	1	1	1	1	1	1	1
1	0	0	0	1	0	1	0	1
0	1	1	1	1	1	1	1	1
0	1	0	1	0	0	1	0	1
0	0	1	1	1	1	0	1	1
0	0	0	1	1	1	0	1	1

All the above are logical implication because in last column we get the column as tautology so by this logical implication is verified in the truth table.

4.  Let  A = { 1 ,{ 1 } , { 2 } }

            Which of the following statements are true?

 a) 1 Є A                             b ) { 1 } Є A   

c) { 1 } C A                         d) {{ 1 }} C A

e) { 2 } Є A                          f) { 2 } C A

g) {{ 2 }} C A                      h) {{ 2 }} C A

a)    1 Є A                        - True

b)   { 1 } Є A                   - True

c)    { 1 } C A                   - True

d)   {{ 1 }} C A                - True

e)    { 2 } Є A                   - True                  

f)      { 2 } C A                   - False

g)    {{ 2 }} C A                - True                

h)   {{ 2 }} C A                - False