If we reduce size of training dataset does it decreases bias? I'm a newbie and learning ML. I've a doubt, normally we know we should increase the size of training dataset or should add more data to reduce variance (fairly understood why). Now variance has inverse relationship with bias, so it means when we're adding more data, we're reducing variance - or we're increasing bias. Then, why this is not possible to reduce bias by reducing the number of training samples. Could someone please explain me.

The variance bias relationship is a causal relationship.
For certain types of bias the variance can reduce when the bias increases. That means that the other way around does not work. If you reduce/increase the variance (by some other means than bias, for instance sample size) then you do not increase/reduce the bias.
A clear example is a shrinkage estimator for estimating the mean of a normal distribution. The typical unbiased estimator is the sample mean $\bar{x}$, which has a variance $\frac{\sigma^2}{n}$. We could also use a biased estimate by multiplying the sample mean with a factor $c \cdot \bar{x}$, which has a variance $c^2\frac{\sigma^2}{n}$. By changing the bias $c$ we can decrease the variance, but by changing the variance, for instance by having different $n$, we do not change $c$.
In a more complex situation we could have an interaction between bias and variance. In the previous example the bias is dependent on $c$. There are settings in which we change this parameter based on the observed variance. But often the relationship is in the other direction. The bias is optimised to reduce the mean squared error, and if we have less variance, then we need less bias.
