The necessity of Baptism

In a recent debate, a Protestant referred to Mark 16:16 in an attempt to show that Baptism is not necessary for our salvation.

As translated in the Revised Standard Version, the verse reads,

• He who believes and is baptized will be saved; but he who does not believe will be condemned. 

This individual pointed to the second clause to make his point.

Let us examine the verse using the tools of symbolic logic.
I will use the following conventions.
Conjunction (and) will be indicated by '&'
Disjunction (or) will be indicated by 'v'.

Implication (if . . .then) will be indicated by '->'.
Negation will be indicated by ~
I will be making reference to The 19 Rules of Inference.

Now, let us define three variables.
A = "One believes"
B = "One is baptized"
C = "One will be saved".

The verse, then, becomes (A & B -> C) & (~A -> ~C)
Let's look at the first phrase first, and, for simplicity's sake, I will define another variable
D=A&B

So, the first phrase is D -> C.
Using transposition, ~C-> ~D .
Material Implication ~Cv D .

Commutation D v ~C.

Now, for D to be true, BOTH A and B must be true.  Such is the meaning of conjunction.
Translating D v ~C into English, therefore, we arrive at "If it is not true that both one is baptized and one believes, one shall not be saved."

Is that consistent with the second clause?

Applying Material implication, ~~A v ~C
Applying Double Negation to the left, A v ~C


Translating into English, One believes, or one will not be saved.

Well, if one believes and is baptized, then one believes.
Therefore, the second clause is included in the first.

In sum, the verse cannot but mean, "Unless you are baptized and you believe, you will not be saved."

Baptism is necessary for our salvation.