Question

Which of the given sets is the set of mathematical eqution? How about the set of inequalitie?

Answer 1

Answer:

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Solution Sets

Solution Sets for Equations

The set containing all the solutions of an equation is called the solution set for that equation.

If an equation has no solutions, we write ∅∅ for the solution set. ∅∅ means the null set (or empty set).

Equation

Solution Set

3x+5=113x+5=11

{2}{2}

x2=xx2=x

{0,1}{0,1}

x+1=1+xx+1=1+x

RR (the set of all real numbers)

x+1=xx+1=x

∅∅ (the empty set)

Sometimes, you may be given a replacement set, and asked to test whether the equation is true for all values in the replacement set.

Example 1:

Find the solution set for the equation z+z=z×zz+z=z×z if the replacement set is {0,1,2,3,}{0,1,2,3,} .

One method of solving this problem is to test all the values in the replacement set using a table.

z0123z+z=z×z0+0=?0×0       0=01+1=?1×1     2≠12+2=?2×2       4=43+3=?3×3       6≠9Result