we know that K=1/1-mpc. but this will only be valid if we consider as=ad

The statement you've provided is related to the concept of the Keynesian multiplier in economics, specifically in the context of the Aggregate Supply (AS) and Aggregate Demand (AD) model.

The Keynesian multiplier (K) is defined as 1/(1-MPC), where MPC is the marginal propensity to consume. This multiplier reflects the idea that an initial change in spending (like government spending or private investment) can lead to a larger change in output.

The condition you've mentioned, AS=AD, is the equilibrium condition in the AS-AD model. This means that the total quantity of goods produced by firms (AS) equals the total quantity of goods purchased by households, firms, the government, and foreigners (AD).

So, the statement "K=1/1-MPC is only valid if AS=AD" is not entirely correct. The formula for the Keynesian multiplier, K=1/(1-MPC), is always valid as it's derived from the concept of the marginal propensity to consume. However, the effect of a change in spending on output (which is what the multiplier measures) will indeed depend on whether the economy is at equilibrium (AS=AD). If the economy is not at equilibrium, changes in spending can lead to changes in prices, interest rates, or other variables, which can affect the size of the multiplier effect.