9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Question

Question

9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

9)For each of the following compound statements, first identify the

corresponding component statements. Then check whether the statements are

true or not.

If a and b are integers, then ab is a rational num

ber.

maths

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Ans)

The component statements are given by

p:a and b are integers.

q: ab is a rational number:.

Since the product of two integers is an integer and therefore a rational number, the

Ifand only if', represented by the symbol,,,- ''means the following equivalent fornis

Compound statement is true.

lor the given statements p and q.

p

() p if and only if q

(ii) q if and only if p

iii, p is necessary and sufficient conditions for q and vice ver

sa

4, p-q

answered by: Vijayan

Add a comment

Answer 2

Similar Homework Help Questions

8)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. (i) If a triangle ABC is equilateral, then it is isosceles.

8)For each of the following compound statements, first identify thecorresponding component statements. Then check whether the statements aretrue or not.(i) If a triangle ABC is equilateral, then it is isosceles.
13)check whether "or" used in the following compound statement is exclusive or inclusive.write the component statements of the compound statement and use them to check whether the compound statement is true or not .justify your answer t: you are wet when

13)check whether "or" used in the following compound statement is exclusive or inclusive.write the component statements of the compound statement and use them to check whether the compound statement is true or not .justify your answer t: you are wet when it rains or you are in a river
Check the following statements that are correct. There is a penalty of 1.5 points for each...

Check the following statements that are correct. There is a penalty of 1.5 points for each incorrect answer. This question is worth 9 points. On this and all other questions, ignore any indication that it is worth 10 points. a. Every bounded subset of the integers has an infimum that is an integer. Ob. Every bounded subset of the rational numbers has an infimum which is a rational number. Oc. Every bounded subset of the rational numbers has an infimum...

Match each of the following with their corresponding statements. Part A 5s and 6s orbitals Check...

Match each of the following with their corresponding statements. Part A 5s and 6s orbitals Check all that apply. Check all that apply. None of these statements are true. They are in the same energy level. They have the same shape. They have the same maximum number of electrons.
e=[(0,1)] Recall that a rational number x = [(a,b)] is positive if ab > 0 in...

e=[(0,1)] Recall that a rational number x = [(a,b)] is positive if ab > 0 in Z and negative if ab < 0 in Z (for any choice of representative (a,b) E x). For x,y EQ we say x <y iff y e(-x) is positive. (a) Show that x <y iff x (-y) is negative. (b) Show that for each x E Q, precisely one of the following three statements is true: x = e, e < x, x<e. (c)...
9) Indicate whether each of the following statements is true or false. If the statement is...

9) Indicate whether each of the following statements is true or false. If the statement is false, rewrite the underlined portion to make it true. (2 points each) a) A change in primary structure always results in a change in tertiary structure. b) The largest force governing protein structure is the hydrophobic effect. c) Protein folding begins with the formation of tertiary structure. d) A heterodimer exhibits quaternary structure; a homodimer does not.

Q#6 (1 point each) For each of the following statements, determine whether it is true or...

Q#6 (1 point each) For each of the following statements, determine whether it is true or false (circle the answer; you don't need to show any work). (a) True or False: x(x2+1)(x2-1) is an improper rational fraction. (b) True or False: The area enclosed between the graphs of y = x3 and y = 4x over (-2,2] is given by the integral 22(x3 – 4x)dx. (c) True or False: The area enclosed between the graphs of x = 2y2 +1...
Identify if each of the following statements about microtubules (MTs) is True or False. (a) True...

Identify if each of the following statements about microtubules (MTs) is True or False. (a) True False The ends of the MTs in cilia are anchored into a basal body. (b) True False A basal body has a "9 + 2" arrangement.
Rational Number *In Java* A rational number is one that can be expressed as the ratio...

Rational Number *In Java* A rational number is one that can be expressed as the ratio of two integers, i.e., a number that can be expressed using a fraction whose numerator and denominator are integers. Examples of rational numbers are 1/2, 3/4 and 2/1. Rational numbers are thus no more than the fractions you've been familiar with since grade school. Rational numbers can be negated, inverted, added, subtracted, multiplied, and divided in the usual manner: The inverse, or reciprocal of...

Decide whether each statement is true or false and explain your reasoning. Give a counter-example...

Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...

9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Homework Answers

Add Answer to:
9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Post as a guest

Earn Coins

8)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. (i) If a triangle ABC is equilateral, then it is isosceles.

13)check whether "or" used in the following compound statement is exclusive or inclusive.write the component statements of the compound statement and use them to check whether the compound statement is true or not .justify your answer t: you are wet when

Check the following statements that are correct. There is a penalty of 1.5 points for each...

Match each of the following with their corresponding statements. Part A 5s and 6s orbitals Check...

e=[(0,1)] Recall that a rational number x = [(a,b)] is positive if ab > 0 in...

9) Indicate whether each of the following statements is true or false. If the statement is...

Q#6 (1 point each) For each of the following statements, determine whether it is true or...

Identify if each of the following statements about microtubules (MTs) is True or False. (a) True...

Rational Number In Java A rational number is one that can be expressed as the ratio...

Decide whether each statement is true or false and explain your reasoning. Give a counter-example...

9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Homework Answers

Add Answer to: 9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

Post as a guest

Earn Coins

Add Answer to:
9)For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.