Bissoy.com
Doctors Medicines MCQs Q&A

Consider the following statements : A = If n is even, then n2 is even. B = If n2 is not even, n is not even. C = If n2 is even, then n is even. D = If n is not even, then n2 is not even. Which of the following statements is true?

Consider the following statements : A = If n is even, then n2 is even. B = If n2 is not even, n is not even. C = If n2 is even, then n is even. D = If n is not even, then n2 is not even. Which of the following statements is true? Correct Answer C is converse of A.

Mathematical reasoning is a topic of mathematics which deals with truthfulness and falsehood of a statement. A statement is a sentence which is either true or false, but can not be both at the same time. There are certain terms that are frequently used in mathematical reasoning:

  • Inverse: The conditional statement “~p → ~q” is called the inverse of the conditional statement “ p → q ”, where (~ p) and (~ q) means 'not p' and 'not q' respectively. For example, if 'n is not even, n2 is not even' is the inverse of 'if n is even, n2 is even.'
  • Converse: The conditional statement “q → p” is called the converse of the conditional statement “ p → q ”. Example, 'if n2 is even, then n is even' is the converse of 'If n is even, then n2 is even'.
  • Contrapositive: The statement “(~ q) → (~ p)” is called the contrapositive of the statement p → q. For example, 'If n2 is not even, then n is not even' is contrapositive of 'If n is even, then n2 is even'

Hence, we conclude that the above relation is of contraposition.

Related Questions

From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.
Two processes X and Y need to access a critical section. Consider the following synchronization construct used by both the processes Process ? /* other code for process ? */ while(true) { varP = true; while(varQ == true) { /* Critical Section */ varP = false; } } /* other code for process ?? */   Process ? /* other code for process ? */ while(true) { varQ = true; while(varP == true) { /* Critical Section */ varQ = false; } } /* other code for process ? */   Here, varP and varQ are shared variables and both are initialized to false. Which one of the following statements is true?
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. All prime are even. II. Some even are odd. Conclusions: I. Some odd are prime. II. All odd are even. III. No odd is prime.
The logic problems in this set present you with three true statements: Fact 1, Fact 2 and Fact 3. Then you are given three more statements (labelled I, II, III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; or none of the statements could be true. Fact 1: Most stuffed toys are stuffed with beans. Fact 2: There are stuffed bears and stuffed tigers. Fact 3: Some chairs are stuffed with beans. If the fist three statements are facts, which of the following statement/(s) must also be a fact? I. Only children's chairs are stuffed with beans. II. All stuffed tigers are stuffed with beans. III. Stuffed monkeys are not stuffed with beans. Choose the correct answer from the options given below:
The logic problems in this set present you with three true statements: Fact 1, Fact 2 and Fact 3. Then you are given three more statements (labelled I, II, III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; or none of the statements could be true. Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs. If the first three statements are facts, which of the following statement/(s) must also be a fact? I. All birds lay eggs. II. Hens are birds. III. Some chickens are not hens. Choose the correct answer from the options given below: 
The logic problems in this set present you with three true statements: Fact 1, Fact 2 and Fact 3. Then you are given three more statements (labelled I, II, III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; or none of the statements could be true. Fact 1: Pictures can tell a story. Fact 2: All storybooks have pictures. Fact 3: Some storybooks have both words and pictures. If the first three statements are facts, which of the following statement/(s) must also be a fact? I. Pictures can tell a story better than words can. II. The stories in storybooks are very simple. III. Some storybooks have both words and pictures. Choose the correct answer from the options given below:
The logic problems in this set present you with three true statements: Fact 1, Fact 2 and Fact 3. Then you are given three more statements (labelled I, II, III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; or none of the statements could be true. Fact 1: All hats have brims. Fact 2: There are black hats and blue hats. Fact 3: Baseball caps are hats. If the first three statements are facts, which of the following statement/(s) must also be a fact? I. All caps have brims. II. Some baseball caps are blue. III. Baseball caps have no brims. Choose the correct answer from the options given below:
The logic problems in this set present you with three true statements: Fact 1, Fact 2 and Fact 3. Then you are given three more statements (labelled I, II, III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; or none of the statements could be true. Fact 1: Jessica has four children. Fact 2: Two of the children have blue eyes and two of the children have brown eyes. Fact 3: Half of the children are girls. If the fist three statements are facts, which of the following statement/(s) must also be a fact? I. At least one girl has blue eyes. II. Two of the children are boys. III. The boys have brown eyes. Choose the correct answer from the options given below:
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All statements are answers. Some statements are questions. Conclusions: I. No question is a statement. II. Some answers are statements. III. Some questions are statements.
In the question given below are given some statements followed by some conclusions based on those statements. Consider the given statements to be true even if they differ from commonly known facts. Read all the conclusions and then determine which of the given conclusions are rational based on the given statements. Statements: I. No J is R. II. No R is W. III. All W are K. Conclusions: I. No K is R. II. No R is J III. Some W is not R.