## proof

Using simple properties of integers and of l.c.m. and h.c.f. we can easily show that axioms (1)-(3) given in the definition of a Boolean algebra are satisfied. Now axiom (4) will hold if and only if for any a ϵ B, a and n/a have no common factor, other than 1. This condition is equivalent […]

## Let B be the set of all positive integers which are divisors of

Let B be the set of all positive integers which are divisors of 70; i.e., B = {1, 2, 5, 7, 10, 14, 35, 70}. For any a, b ϵ B, let a + b = l.c.m of a, b; a ∙ b = h.c.f. of a, b and a’ = ⁷<span style=’font-size: 50%’>/₀. Then […]

## Let A be a non-empty set and P(A) be the power set of A.

Let A be a non-empty set and P(A) be the power set of A. Then P(A) is a Boolean algebra under the usual operations of union, intersection and complementary in P(A). The sets ∅ and A are the zero element and unit element of the Boolean algebra P(A). Observe that if A is an infinite […]

## FREQUENCY DISTRIBUTION

FREQUENCY DISTRIBUTION A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class. How do we develop a frequency distribution? The following example shows the steps to construct a frequency distribution. Remember, our goal is to construct tables, charts, and graphs that will quickly summarize the […]

## DESCRIBING DATA

DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION 25 (a) Is the data qualitative or quantitative? Why? (b) What is the table called? What does it show? (c) Develop a bar chart to depict the information. (d) Develop a pie chart using the relative frequencies. The answers to the odd-numbered exercises are at the […]

## DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION 23

DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION 23 Pie and bar charts both serve to illustrate frequency and relative frequency ta- bles. When is a pie chart preferred to a bar chart? In most cases, pie charts are used to show and compare the relative differences in the percentage of observations for each […]

## A set of multiple choice intermediate algebra questions,

A set of multiple choice intermediate algebra questions, If f(x) = 4×3 – 4×2 + 10, then f(-2) = A. 26 B. -38 C. 10 D. 38 2. Which of these values of x satisfies the inequality -7x + 6 ≤ -8 A. -2 B. 0 C. -7 D. 2 The domain of the function f(x) = √(6 – 2x) is […]

## Intermediate Algebra Questions

Intermediate Algebra Questions Write 1.5 × 10-5 in standard form. Evaluate: 30 – |-x + 6| for x = 10 Evaluate: 2xy3 + x – 2y for x = 2 and y = -2 What is the slope of the line perpendicular to the line y = – 4 Write an equation of the line with slope 2 […]

## True/False Algebra Questions

True/False Algebra Questions (True or False)     The inequality |x + 1| < 0 has no solution. (True or False)     If a and b are negative numbers, and |a| < |b|, then b – a is negative. (True or False)     The equation 2x + 7 = 2(x + 5) has one solution. (True […]