hhhhQUESTION BANKBBM-104BASIC MATHEMATICSDepartment of ManagementFaculty of Social SciencesSession: 2017-2018Revised July,2017UNIT I: DISCRETE MATHEMATICS1.Using the statements P: Mohan is honest, Q: Mohan is poor , R: The triangle isisosceles, S: Two sides of the triangle are equalWrite the following molecular statements in symbolic form:(a)Mohan is poor but honest.(b) Mohan is rich but dishonest.(c)Mohan is neither rich nor honest.(d) Mohan is poor or he is both rich and dishonest.(e)If the triangle is isosceles then two sides of the triangle are of equal length.(f)If the two sides of the triangle are not equal then the triangle is not isosceles.(g) It is not true that if Mohan is poor then he is honest.(h) If Mohan is poor then if he is honest then it is not true that the triangle isisosceles.(i)If either Mohan is poor or Mohan is honest, then Mohan is not dishonest.2. Construct the truth tables for the following formulas:(a) (PQ) (b) P(QP) (c) (P(PQ)Q) (d) (PQ)(PQ) 3.Prove the equivalence of the following statements:(a) P(QR) , P (QR) (b) ~(P Q) , ~ Q ~P 4.If P and Q are false and R and S are true then find the truth values of :(a) P(QR) P(QP) (b) (()())(~)PQQRSQ5. Formulate the symbolic expressions in words using:P: Today is Sunday, Q: It is not raining, R: It is hot6.Define the following:7.Prove the following set identities:(a)A – (AB) = A - B (c) (A B)c= AcBc8.In how many ways 5 passengers can sit in a compartment having 16 seats?9.In how many ways 5 girls and 3 boys can be seated in a row so that all the boys sittogether?10. How many numbers lying between 100 and 1000 can be formed using the digits1,4,5,6,7,0?11. How many committees of 5 persons consisting of at least 3 men can be formed from agroup of 10 men and 7 women?12. How many 8-lettered words can be formed from the letters of ‘COURTESY’ thatbegin with C and end with Y.
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