Writing statements into symbols Discrete Math.The variable x represents students, F(x) means "x is a...

Step 1
(a) Some freshmen are math majors ∼ There exist x such that (x is a Freshman and x is a math major): $\mathrm{\exists }F(F(x)\wedge M(x))$
Step 2
(b) Every math major is a freshman. ∼ For all x (if x is a math major, then x is a Freshman.) $\mathrm{\forall }x(M(x)\to F(x))$
Step 3
(c): No math major is a freshman. ∼ There does not exist an x such that (x is a math major and x is a freshman).
$\begin{array}{rl}\mathrm{\neg }\mathrm{\exists }x(M(x)\wedge F(x))& \equiv \mathrm{\forall }x(\mathrm{\neg }M(x)\vee \mathrm{\neg }F(x))\\ \\ & \equiv \mathrm{\forall }x(M(x)\to \mathrm{\neg }F(x))\end{array}$