Why is it necessary to use the sigmoid activation function in logistic regression instead of a linear activation function?

Group of answer choices

Without the sigmoid activation function, logistic regression would not be able to handle binary classification tasks effectively.

Logistic regression inherently assumes a linear relationship between input features and the log$-$odds of the target variable, necessitating the use of the sigmoid function for proper transformation.

The sigmoid activation function ensures that the output of logistic regression is bounded between $0$ and $1,$ which aligns with the interpretation of probabilities.

The sigmoid activation function introduces non$-$linearity, allowing logistic regression to model complex relationships between input features and the probability of the target class.

A linear activation function in logistic regression would result in unstable gradients during training, leading to convergence issues.