5. a) Determine the converse, inverse and contrapositive of thefollowing 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) hand 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 theX-1inverse of the above function if it exists, where R is the set ofreal numbers. 6. Given the Boolean function:a) F(P,Q, R)= PQR+ PQR + PQR+ PQR + PQR+ PQRi)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 setA = {l SxS 12}. Find the reflexive, symmetric andtransitive closure of this relation?c) A customer at an ATM realizes that he has forgotten the last twodigits of his pin code. He however remembers that the two digitswere greater than five. He does have 3 entry tries before theATM confiscates his card.How many possible combinations of the 2 digits can he try?

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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 (iii) If 9x +36 = 9 then x+ 17. (iv) If cos(x) =1 then x= 0.

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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