Discrete Mathematics Answers

What and Define Probability and cost considerations in project scheduling in mathematical foundations of computer science

What and Define arrow diagram in mathematical foundations of computer science

Assignment problems in mathematics foundations of computer science

Prove that If A and B are any sets with the property that there is a one-to-one function from A to B and a one-to-one function from B to A, then A and B have the same cardinality.

 Let 8Z be the set of all integers that are multiples of 8. Prove that 8Z has the same cardinality as 3Z, the set of all integers multiples of 3. 

Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c

is an equivalence relation.

Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric,

and transitive.

Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c is an equivalence relation. Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.

a)     Suppose P (x, y) denotes the equation8, what will the truth values of the Propositions P (2,2), P (0,4).

The following table shows the income distribution of 600 families. Find the minimum income

of the riches 30% families. Also the limits of income of middle 50% of families, to the nearest

rupees.

Income Below

75

75-

150

150-

225

225-

300

300-

375

375-

400

400 &

above

No. of

families

69 137 225 46 88 25 10

Ans.: the richest 30 % families earns Rs. 222 and above per week , the middle 50% families

weekly income lies between 120 and 256.

How many different plates are there that involve 1, 2 or 3 letters followed by 1,

2, 3 or 4 digits?

How many 2 digit or 3-digit numbers can be formed using the digits 1, 3, 4, 5, 6,

8 and 9 if no repetition is allowed?