Intuitive explanation for p ∨ q → r ≡ ( p → r) ∧ (q → r) Although, it is possible to prove the above equivalence using truth tables, I don't know how to prove it without using truth tables.Can someone explain it in plain english?

This is a neat little identity. I would put it like this: there's a red button that sets off the bomb. If either Angie or Bill pushes it, then the bomb will go off.
$$(\text{Angie pushes the button}) \vee (\text{Bill pushes the button}) \implies (\text{explosion})$$
But we also know that, independently, if Angie pushes the button then the bomb will go off and if Bill pushes the button, the bomb will go off.
$$
((\text{Angie pushes the button}) \implies (\text{explosion}))
\wedge
((\text{Bill pushes the button} \implies (\text{explosion}))$$
