Math Reasoning.pdf

(i) "There are 35 days in a month" is a statement, (ii) "Mathematics is difficult" is not a statement, (iii) "The sum of 5 and 7 is greater than 10" is a statement, (iv) "The square of a number is an even number" is not a statement, (v) "The sides of a quadrilateral have equal length" is not a statement, (vi) "Answer this question" is not a statement, (vii) "The product of 1/4 and 8 is 8" is a statement, (viii) "The sum of all interior angles of a triangle is 180°" is a statement, (ix) "Today is a windy day" is not a statement, (x) "All real numbers are complex numbers" is a statement.
Three examples of sentences which are not statements are: (i) "x is always greater than 1", (ii) "He is an engineer", (iii) "Mathematics is Easy".
Negations of given statements are: (i) "Chennai is not the capital of Tamil Nadu", (ii) "1/2 is a complex number", (iii) "All triangles are equilateral triangles", (iv) "The number 7 is not greater than 8", (v) "Every natural number is not an integer".
Given pairs of statements are negations of each other.
Component statements of given compound statements are: (i) p: Number 3 is prime, q: Number 3 is odd, (ii) p: All integers are positive, q: All integers are negative, (iii) p: 100 is divisible by 3, q: 100 is divisible by 11, r: 100 is divisible by 5.