The proposition p ∧(~p ∨ q) is:

Let p and q be propositions. Using only the truth table decide whether p ⇔ q does not imply p → q is true or false.

A language with string manipulation facilities uses the following operations

 head(s): first character of a string
 tail(s): all but the first character of a string
 concat(s1,s2):s1 s2
 for the string acbc what will be the output of
 concat(head(s), head(tail(tail(s)))) 

If the proposition ¬p ⇒ ν is true, then the truth value of the proposition ¬p ∨ (p ⇒ q), where ¬ is negation, ‘∨’ is inclusive or and ⇒ is implication, is

Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: If F₁, F₂ and F₃ are propositional formulae such that F₁ ∧ F₂ → F₃ and F₁ ∧ F₁ → ~F₂ are both tautologies, then which of the following is true: