Answer: The negation of the statement: p: a + b = b + a is a true for every real number a and b. ~p: There exist real numbers are ‘a’ and ‘b’ for which a+b ≠ b+a. The statement is not the negation...

Answer: The negation of the statement: r: There exists a number x such that 0 < x < 1. ~r: For every real number x, either x ≤ 0 or x ≥ 1.

Answers: (i)  The negation of the statement: p: For every positive real number x, the number (x – 1) is also positive. ~p: There exists a positive real number x, such that the number (x – 1) is not...

Answers: (i) “The number x is an irrational number.” The statement “The number x is not a rational number.” It is a negation of the first statement. (ii) “The number x is an irrational number.” The...

Answers: (i)  The negation of the statement is: “There is at least one rectangle whose both diagonals do not have the same length.” (ii) The negation of the statement is: “No policemen are...

Answers: (i)  The negation of the statement is: It is false that “complex numbers are not a real number.” [Or] “All complex number are real numbers.” (ii)  The negation of the statement is: “I will...

Answers: (i)  The negation of the statement is: It is false that “All birds sing.” [Or] “All birds do not sing.” (ii)  The negation of the statement is: It is false that “even integers are prime.”...

Answer: The negation of the statement is: It is false that “The sun is cold.” [Or] “The sun is not cold.”

Answers: (i) The negation of the statement is: It is false that “Ravish is honest.” [Or] “Ravish is not honest.” (ii)  The negation of the statement is: It is false that “The earth is round.” [Or]...

Answers: (i)  The negation of the statement is: It is false that “Bangalore is the capital of Karnataka.” [Or] “Bangalore is not the capital of Karnataka.” (ii)  The negation of the statement is: It...