5. a) Determine the converse, inverse and contrapositive of the following statements by indicating the conditional statement. (i) If we are in binary system then 1 + 1 = 10 (ii) Good food are not cheap (iii) If 9x +36 = 9 then x+ 17. (iv) If cos(x) =1 then x= 0.

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Chapter2: Second-order Linear Odes
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5. a) Determine the converse, inverse and contrapositive of the
following statements by indicating the conditional statement.
(i)
If we are in binary system then 1 + 1 = 10
(ii)
Good food are not cheap
(ii)
If 9x +36 = 9 then x # 17.
(iv) If cos(x) =1 then x = 0.
b) If f(x) = 8x, g(x)=x*and h(x) = 4x +3 then find (f°g) h
and f(g h). Show that (f °g) h= f •(g•h)?
c) Let f:R→(-1, 1) be defined by f(x) =
-,xe R . Find the
X-1
inverse of the above function if it exists, where R is the set of
real numbers.
Transcribed Image Text:5. a) Determine the converse, inverse and contrapositive of the following statements by indicating the conditional statement. (i) If we are in binary system then 1 + 1 = 10 (ii) Good food are not cheap (ii) If 9x +36 = 9 then x # 17. (iv) If cos(x) =1 then x = 0. b) If f(x) = 8x, g(x)=x*and h(x) = 4x +3 then find (f°g) h and f(g h). Show that (f °g) h= f •(g•h)? c) Let f:R→(-1, 1) be defined by f(x) = -,xe R . Find the X-1 inverse of the above function if it exists, where R is the set of real numbers.
6. Given the Boolean function:
a) F(P,Q, R)= PQR+ PQR + PQR+ PQR + PQR+ PQR
i)
Represent the function in a Karnaugh Map and minimize?
ii)
Draw the minimized digital circuit?
b) A relation R = {(x, y): 4x = 6y} is de fined on the set
A = {l SxS 12}. Find the reflexive, symmetric and
transitive closure of this relation?
c) A customer at an ATM realizes that he has forgotten the last two
digits of his pin code. He however remembers that the two digits
were greater than five. He does have 3 entry tries before the
ATM confiscates his card.
How many possible combinations of the 2 digits can he try?
Transcribed Image Text:6. Given the Boolean function: a) F(P,Q, R)= PQR+ PQR + PQR+ PQR + PQR+ PQR i) Represent the function in a Karnaugh Map and minimize? ii) Draw the minimized digital circuit? b) A relation R = {(x, y): 4x = 6y} is de fined on the set A = {l SxS 12}. Find the reflexive, symmetric and transitive closure of this relation? c) A customer at an ATM realizes that he has forgotten the last two digits of his pin code. He however remembers that the two digits were greater than five. He does have 3 entry tries before the ATM confiscates his card. How many possible combinations of the 2 digits can he try?
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