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a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain the partition of V induced by R.
b) Let A = {1, 2, 3, 4} and define R on P(A) -{Ø} by xRy iff x ∩y ≠Ø. Is R an equivalence relation? Describe
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
Determine y′′ for x 2 + y 4 = 10 Solution: We know that to get the second derivative we required the first derivative and to get that w
Larry purchased 3 pairs of pants for $24 each or have 5 shirts for $18 each. How much did Larry spend? Divide the miles through the time to find the rate; 3,060 ÷ 5 = 612 mph.
Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT
Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some
AREAS RELATED TO CIRCLES The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. In t
why it is hard?
Peter was 60 inches tall on his thirteenth birthday. By the time he turned 15, his height had increased 15%. How tall was Peter when he turned 15? Find 15% of 60 inches and add
formules
Arc Length - Applications of integrals In this part we are going to look at determining the arc length of a function. As it's sufficiently easy to derive the formulas that we'
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