Commutative law

Write the component statements of the following compound statements and check whether the compound statement is true or false (i) Venus is the smallest and Jupiter is the largest planet of solar system. (ii) India is a country and Asia is a continent. (iii) Commutative law holds for addition and subtraction of rational number. (iv) Additive inverse exists for natural number and rational number (v) 32 is a multiple of 2, 3 and 4.

Write the component statements of the following compound statements and check whether the compound statement is true or false · (i) Venus is the smallest and. Jupiter is the largest planet of solar system. (ii) India is a country and Asia is a continent. (iii) Commutative law holds for addition and subtraction of rauonal number. (iv) Additive inverse exists for natural number and rational nutnber (v) 32 is a multiple of 2, 3 and 4.

In the case of irrational numbers - (i) State the commutative law for addition . By . Taking any 2 irrational numbers, prove the law, State the commutative law of multiplication By taking any 2 irrational numbers, prove the law,

Commutative and associative

Non commutative and distributive law

a.a=|a|^(2) and commutative and distributive law of dot product

Define scalar product of two vectors . Show of two vectors . Show that scalar product of vectors satisfies the commutative and distributive laws.

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

Prove that the operaton ** on QQ-{1} given by a*b=a+b-ab for all a,binQQ-{1} (i) is closed: (ii) satisfies the commutative and associative laws, (iii) Find the identity element, (iv) Find the inverse of any element ainQQ-{1}.