Question

Type a proposition involving p, q, r and s that is true just when at least two of the propositional variables are true. For example, your proposition would be true in any case for which p and r are both true but false when, say, p is true while q, r and s are all false.

Answer 1

But we need the proposition involving the variables p,q,r & s that is true when atleast two of the variables are true.

We can make the desired proposition by using .

Since we desire atleast two of variables true.Let us make every possible pair of all of the variables.Since is true when both p and q are true.Using this "tone" we can make the pro​​​​position,

Since,in this proposition, suppose if only 'p' variable is true and other variables are false,then will give result in False with every variables other than p.So resulting proposition P will be false.

If any two of the proposition will be true,(Suppose 'r' and 's' are true) then   will give us result True.So the Compound proposition P will be true.So Our required proposition is

which will is True when atleast two of the variable are true.