Logical Operations in Mathematics Quiz

Answer: Subtraction

First an explanation of the solution. The correct matches can be obtained logically from just these clues. It may be possible that one gets the solution through a different order of applying the clues.

Firstly, arranging the words alphabetically, we have
Addition, Combination, Differentiation, Division, Equation, Integration, Inversion, Multiplication, Permutation and Subtraction.

'Addition', 'Division', and 'Equation' have 8 letters; 'Inversion' has 9 letters; 'Subtraction', 'Integration', 'Permutation', and 'Combination' have 11 letters; 'Multiplication' has 14 letters; and 'Differentiation' has 15 letters.

The statement for Operation 5 implies that it ends in "-sion". Thus it must be 'Division' or 'Inversion'. The statement for Operation 10 states that it has the same number of letters as Operation 5, but 'Inversion' is the only word with 9 letters. Therefore, Operation 5 must be 'Division'.

The statement for Operation 6 states that it starts with the same letter as Operation 5. Therefore, Operation 6 must be 'Differentiation'. Operation 10 has to be 8 letters long, and is therefore 'Addition' or 'Equation'. However, the clue for Operation 7 states that it comes alphabetically before Operation 10. 'Addition' is the word that comes alphabetically before any other word. Thus, Operation 10 cannot be 'Addition'. Operation 10 must be 'Equation'.

Operation 7, which comes alphabetically before Operation 10, must be either 'Addition' or 'Combination'. But the statement for Operation 4 says that Operation 4 is alphabetically before Operation 7. Therefore, Operation 4 must be 'Addition'. Operation 7 is 'Combination'.

The clue for Operation 1 states that it begins with a letter in the second half of the alphabet. Therefore, it is either 'Permutation' or 'Subtraction'.

The clue for Operation 8 states that it is longer than Operation 7. Operation 7 is 'Combination', and is 11 letters long. The only two words longer than 'Combination' are 'Differentiation' and 'Multiplication'. As Operation 6 is 'Differentiation', Operation 8 must be 'Multiplication'.

The clue for Operation 3 states that it is alphabetically just after Operation 8. Therefore, Operation 3 must be 'Permutation'. Now that Operation 3 is 'Permutation', Operation 1 must be 'Subtraction'.

Finally, the clue for Operation 2 states that it has an unique number of letters in it. The two words remaining are 'Inversion' and 'Integration'. 'Inversion' is the only word that has 9 letters, while there are 4 words in all which have 11 letters. This matches Operation 2 to 'Inversion'.

The only remaining one, Operation 9, must be 'Integration'. That's it! All options matched!


The basic definition of subtraction is the taking away of a number called the subtrahend from a number called a minuend. It is denoted by a minus sign. The notion of subtraction can be extended to the taking away of one or more objects from a group.

Answer: Inversion

The word inversion mostly refers to an operation in linear algebra. A square matrix is a matrix with same number of rows and columns. Matrix division is not defined directly. However, the inverse of a square matrix is the matrix a matrix must be multiplied with to get the identity matrix of order 'n', where 'n' is the number of rows and columns. Finding out the inverse of a matrix is called inversion.

Answer: Permutation

Permutation refers to the act of selecting a number of objects from a group and arranging them. The number of permutations of 'r' objects from 'n' objects refers to the number of ways we can select 'r' of the 'n' objects as well as arrange them. The order of the objects does matter. If n! denotes the product of the natural numbers 1 to n, the number of permutations of 'r' objects from 'n' objects is defined as the quotient when n! is divided by (n-r)!.

Answer: Addition

Addition is regarded as the most basic of mathematical operations. Adding two quantities refers to finding out their total. This operation is shown by a plus sign. The operation can be extended to integers, complex numbers or even matrices.

Answer: Division

The basic definition of division is the act of counting how many times a given number 'a' is contained in a number 'b'. The number 'c' obtained is the result when 'b' is divided by 'a'. If no number is left over on division, the dividend 'b' is said to be perfectly divisible by the divisor 'a'. If a number is left over, it is known as the remainder. Division is not defined for vectors. Division in complex numbers is actually multiplication with the multiplicative inverse.

Answer: Differentiation

Differentiation is the principal operation used in differential calculus. Differential calculus studies the rate of change of functions. A differential of a quantity refers to a infinitely small change in the quantity. Differentiation refers to finding out the instantaneous slope of a function at a point.

This instantaneous slope is called the derivative. It is denoted as f'(x) or dy/dx. The exponential function is a function whose differentiation gives us the same function.

Answer: Combination

Combination refers to the number of ways of selecting some objects from a group. The order of the objects is not important. If 'r' objects are to be selected from 'n' objects, the number of combinations is the quotient when the factorial of 'n' is divided by the product of the factorial of 'r' and the factorial of 'n-r'.

The factorial of a number is the product of the natural numbers from 1 to that number.

Answer: Multiplication

For whole numbers, multiplication is defined as the repeated addition of one number. The number added repeatedly is called the multiple and the number of times it is added is the multiplier. The operation can be extended to complex numbers, or matrices. In vectors, two types of multiplication are defined, the scalar dot product and the vector cross product.

Answer: Integration

Integration can be defined as the opposite process of differentiation. The anti-derivative of the derivative of a function gives back the function, along with an arbitrary constant. Finding out the anti-derivative is called integration. It can be both definite or indefinite. Definite integration, i.e., integration between two limits, is equivalent to finding out the area under a graph.

The two definitions of integration are connected by the Newton-Liebniz formula.

Answer: Equation

Equation is both the process as well as the statement of making two things equal to each other. It is denoted by an 'is equal to' sign. An equation can be linear, quadratic, cubic and so on, based on the highest degree of the unknown variable. An equation remains when same things are added, subtracted or multiplied on both sides. Division by a non-zero number also maintains an equation.