Question Two
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine,
(i) A × B
(ii) B × A
(iii) Is A × B = B × A?
(iv) Is n (A × B) = n (B × A)?
(8 Marks)
Question Three
Determine whether each of the following form is a tautology Or a contradiction Or neither:
i) PQPQ
ii) PQPQ
iii) PQPQ
(9 Marks)
Question Four
Using principle of mathematical induction prove that
(1 + 2 + 3 + ... + n = n (n + 1) / 2 ( 3 Marks)
Answers
Answered by
3
Step-by-step explanation:
Given sets are A = {1, 2, 3, 4} and
B = {5, 7, 9}
1)A×B={1, 2, 3, 4} ×{5, 7, 9}
=>A×B={(1,5),(1,7),(1,9),(2,5),(2,7),(2,9),. (3,5),(3,7),(3,9),(4,5),(4,7),(4,9)}--------(1)
n(A×B)=12-------(2)
B×A={5, 7, 9}×{1, 2, 3, 4}
=>{(5,1),(5,2),(5,3),(5,4),(7,1),(7,2),(7,3),(7,4),(9,1),(9,2),(9,3),(9,4)}--------(3)
n(B×A)=12------(4)
From (1)&(3)
A×B≠B×A
from(2)&(4)
n(A×B)=n(B×A)
2)Given that
1+2+3+---+n=n(n+1)/2
Put n=1 then
LHS=1
RHS=1(1+1)/2=2/2=1
LHS=RHS is true for n=1
now put n=k then 1+2+3+---+K=K(K+1)/2
LHS =RHS is true for n=k
now put n=k+1 then
LHS=1+2+3----(k+1)
RHS=(k+1)(k+1+1)/2
=>(k+1)(k+2)/2
LHS =RHS is true for n=k+1
1+2+3+---+n=n(n+1)/2
Answered by
0
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