Design a DFA that accepts strings containing 1010 as substring.

Design a DFA that accepts strings containing 1010 as substring.
We know from DFA,
A = (Q, Σ, δ, q₀, F)
Now,

Here,
Q: Finite set of states
Σ: Input symbols
δ: Transition function
q₀: Initial state
F: Final state
∴ A = ({q₀, q₁, q₂, q₃, q₄}, {0, 1}, δ, q₀, {q₄})

Now, transition function for 1010,
δ ̂ (q₀, ϵ) = q_0
δ ̂ (q₀, 1) = δ (δ ̂ (q₀, ϵ), 1) = δ (q₀, 1) = q₁
δ ̂ (q₀, 10) = δ (δ ̂ (q₀, 1), 0) = δ (q₁, 0) = q₂
δ ̂ (q₀, 101) = δ (δ ̂ (q₀, 10), 1) = δ (q₂, 1) = q₃
δ ̂ (q₀, 1010) = δ (δ ̂ (q₀, 101), 0) = δ (q₃, 0) = q₄