Statements and Sets Fill in the blanks

Exercise - 1















2. Write the conjunction and disjunction of the given statements.
(i) 5 is an odd number; 5 is positive
5 is an odd number or 5 is positive.
5 is an odd number and 5 is positive.
Similarly we can write it for (ii),(iii),(iv) and (v)

3. Write each of the following statements using the appropriate connectives ^,V,=>,<=>,~. And state their truth values.

(i)5+7=10 and 4+3=7
5+7=10 ^ 4+3=7
F ^ T= F

(ii) 7 is odd or 7 is prime
7 is odd v 7 is prime
T V T = T

(iii) If x+2=0 then x=-2
If then means implication
x+2=0 => x=-2
T => T = T

(iv) x+2=0 iff x=-2
Biimplication
x+2=0 <=> x=-2
T <=> T = T

(V) 7 not equal to 10
~(7=10)- T

4. Rewrite the following statements using the connective symbols. Here p, q are any two statements.

(i) notp
~p
(ii) p or q
p V q

(iii) p and q
p ^ q

(iv) p only if q
p => q

(v)p iff q
p <=> q

(vi) p and not q
p^(~q)

(vii) (~p) or q
(~p)Vq

(viii)(either p) or (not p)
(either p)V(~p)

(ix) p or not p
pV(~p)

(x)(not p) and (not q)
(~p)^(~q)





















6. State the truth values of the following disjunctions
(i) 4+3=7 or 5x4=21
T ^ F = T
1 + 0 = 1
(ii) 4 divided by 2=1 or 2 divided by 1 = 4
F ^ F = F
0 + 0 =0
(iii) 3 divided by 2=1 or 3x2=6
F^T=T
0 + 1 = 1
(iv) 4x5=20 or 4 divided by 2 = 2
T^T=T
1 + 1 = 1

7.State the truth values of the following conjunctions.
(i) 20 divided by 10=2 and 20x10=200
T v T = T
1 x 1 =1
(ii) 10+2=12 and 10 divided by 2 =5
T v T = T
1 x 1 =1
(iii) 10+15 = 20 and 15-10=5
F v T = F
0 x 1 = 0
(iv) 15x3=45 and 15+3=20
F v F = F
0 x 0 = 0

8.State the truth values of the following implications.
(i)If 3+2=5 then 1x0=0
T => T = T
(ii) If 3x6=20 then 2+7=9
F => T = T
(iii) If 5x7=30 then 2 divided by 1=2
F => T = T
(iv) If 6x7=42 then 6 divided by 2=4
T => F= F

9.State which of the following are true statements
(i) 4+3=10 <=> 4x3=12
F <=> T = F
(ii) 4x7=20 <=> 4 divided by 7=1
F <=> F = T
(iii) 5x8=40 <=> 8-2=5
T <=> F = F
(iv)6-3=3 <=> 6x3=18
T <=> T = T

10. Write the converse, inverse and contrapositive of the following conditions.
(i) If two triangles are congruent then they are similar.
Converse: If two triangles are similar then they are congruent.
Inverse: If two triangles are not congruent then they are not similar.
Contrapositive: If two triangles are not similar then they are not congruent.

(ii) If in a triangle ABC, AB=AC then AngleB=AngleC
Converse: If in a triangle ABC, AngleB=AngleC then AB=AC.
Inverse:If in a triangle ABC, AB not equal to AC then AngleB not equal to AngleC.
Contrapositive: If in a triangle ABC, AngleB not equal to AngleC then AB not equal to AC.
Similarly we can do the rest.

11. Let p be "She is beautiful" and q be "She is happy". Write each of the following Statements that are in symbolic form into english sentences.
(i)p ^ q
She is beautiful and she is happy.
Similarly we can do the rest.