A design support apparatus includes: a logical expression substitution unit to substitute a part of the logical expression, which includes a function expression of the design variables and a quantifier attached to the design variable, with a substitution variable; a quantifier elimination unit to generate a relational expression including the substitution variable and design variables without the quantifier by eliminating the design variable to which the quantifier is attached from the logical expression; a sampling point generation unit to generate a plurality of sampling points corresponding to the design variables and the substitution variable included in the relational expression; a possible range computation unit to compute, for each of the sampling points, a possible range that the relational expression may take, by calculating values of remaining design variables included in the relational expression based on the relational expression; and a possible range display unit to display the possible range.