Assertion (A): Associativity properties of addition of natural numbers holds good.
Reason (R): For natural numbers a, b and c, a + (b + c) = (a + b) + c shows addition of natural numbers is associative.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A): Addition of natural numbers is associative, i.e. for natural numbers a, b and c, a + (b + c) = (a + b) + c. So, the assertion is true.
Reason (R): The relation a + (b + c) = (a + b) + c is exactly the statement of the associative property of addition of natural numbers. So, the reason is true and it correctly explains the assertion.
Both A and R are true.
Hence, option 3 is the correct option.
Assertion (A): 656 × 42 - 656 × 17 = 656 × (42 - 17) = 9850
Reason (R): For any three numbers x, y and z : x × (y - z) = x × y - x × z the multiplication is distributive over subtraction.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A): Using the distributive law, 656 × 42 - 656 × 17 = 656 × (42 - 17) = 656 × 25 = 16400, not 9850. So, the assertion is false.
Reason (R): For any three numbers x, y and z, x × (y - z) = x × y - x × z, which is the distributive property of multiplication over subtraction. So, the reason is true.
A is false and R is true.
Hence, option 2 is the correct option.