Proof by Contradiction Quiz

Identify the negation of the statement: 'All prime numbers are odd'

• All prime numbers are even

• Some prime numbers are even

• Not all prime numbers are odd

• No prime numbers are odd

Identify the negation of the statement: 'If x is a rational number, then x^2 is also a rational number'

• There exists a rational number x such that x^2 is not a rational number.

• For all rational numbers x, x^2 is not a rational number

• If x is not a rational number, then x^2 is also not a rational number

• If x is a rational number, then x^2 is not a rational number

Assuming the negation to be true, what can be concluded about the original statement: 'All even numbers are prime'

• The original statement is true.

• The original statement is partially true.

• The original statement is false.

• The original statement is irrelevant.

Assuming the negation to be true, what can be concluded about the original statement: 'If a number is divisible by 3, then it is also divisible by 9'

• The original statement is definitely true

• The original statement is only true for even numbers

• The original statement is only true for prime numbers

• The original statement is not necessarily true.

Conclude whether the original statement is true or false: 'If n^2 is an even number, then n is also an even number'

• True

• Sometimes true

• Not enough information

• False

Conclude whether the original statement is true or false: 'If 2n+1 is an even number, then n is also an even number'

• False

• True

• Sometimes true

• Not enough information

Identify the statement to be proved in the proof by contradiction: 'If a^2 is an even number, then a is also an even number'

• If a^2 is an odd number, then a is also an odd number

• If a^2 is a prime number, then a is also a prime number

• If a^2 is a multiple of 3, then a is also a multiple of 3

• If a^2 is an even number, then a is also an even number

Identify the statement to be proved in the proof by contradiction: 'If 3n+2 is an odd number, then n is also an odd number'

• If 3n+2 is an odd number, then n is also an odd number

• If 3n+2 is an even number, then n is also an even number

• If 3n+2 is an even number, then n is also an odd number

• If 3n+2 is an odd number, then n is also an even number

Explain the concept of contradiction in the context of proof by contradiction

• In proof by contradiction, we assume the opposite of what we want to prove and then show that this assumption leads to a contradiction, which proves that the original statement must be true.

• Contradiction in proof by contradiction means that the statement is neither true nor false

• In proof by contradiction, we assume the original statement is false and then show that it leads to a true conclusion

• Proof by contradiction involves proving a statement by providing multiple contradictory arguments

Explain the concept of contradiction in the context of proof by contradiction

• Proof by contradiction involves proving a statement by providing multiple contradictory arguments

• In proof by contradiction, we assume the opposite of what we want to prove and then show that this assumption leads to a contradiction, which means our original statement must be true.

• Contradiction in proof by contradiction means that the statement is neither true nor false

• In proof by contradiction, we assume the statement we want to prove and then show that it leads to a contradiction