Mathematics
State whether the following statements are true or false. Justify your answers.
(i) All hexagons are polygons.
(ii) Some polygons are pentagons.
(iii) Not all even numbers are divisible by 2.
(iv) Some real numbers are irrational.
(v) Not all real numbers are rational.
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Answer
(i) This statement is true as in geometry a hexagon can be defined as a closed two-dimensional polygon with six sides.
(ii) This statement is true as not all polygons are pentagons.
(iii) This statement is false because every even number is divisible by 2.
(iv) This statement is true because not all real numbers are irrational.
(v) This statement is true because this statement is the same as saying "there is a real number that is irrational". As we know, real numbers can be irrational as well. Hence, the statement is true.
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