Option 1 states that both the assertion (A) and the reason (R) are true, and that R is the correct explanation of A. According to option 4, A is false but R is true. Let`s analyze each statement to understand the correct explanation.

The assertion (A) states that carbon dioxide can be liquefied by applying a pressure equal to 73 atmospheres at temperatures above 31 °C. This statement is incorrect because carbon dioxide cannot be liquefied at temperatures above its critical temperature, which is -56.6 °C for carbon dioxide.

The reason (R) states that a gas can be liquefied by applying critical pressure when it is cooled below its critical temperature. This statement is true. When a gas is cooled below its critical temperature, it reaches a point where no amount of pressure can keep it in its gaseous state, and it will turn into a liquid. This is known as the critical point.

Therefore, the correct explanation is that A is false because carbon dioxide cannot be liquefied at temperatures above its critical temperature, but R is true because the cooling of a gas below its critical temperature allows it to be liquefied by applying critical pressure.

In conclusion, option 4 is the correct answer