`TlCl_(3)` is more stable than `TlCl`.
`+1` oxidation state of thallium us more stable than `+3`.

Explanation

To analyze the statements regarding the stability of thallium compounds, let's break down the question step by step.

### Step 1: Analyze the Stability of TlCl3 vs. TlCl
The first statement claims that TlCl3 (thallium trichloride) is more stable than TlCl (thallium chloride). However, this statement is incorrect.

**Reasoning:**
- Thallium in the +1 oxidation state (Tl+) is more stable than in the +3 oxidation state (Tl3+).
- Therefore, TlCl (which contains Tl+1) is more stable than TlCl3 (which contains Tl+3).

### Step 2: Understanding the Oxidation States of Thallium
The second statement claims that the +1 oxidation state of thallium is more stable than the +3 oxidation state. This statement is true.

**Reasoning:**
- Thallium has a large atomic size, and its electronic configuration is [Xe] 4f14 5d10 6s2 6p1.
- The presence of filled f and d orbitals leads to poor shielding of the nucleus, which causes the 6s electrons to be less involved in bonding. This phenomenon is known as the "inert pair effect."
- As a result, the 6s electrons become inert and do not participate in bonding, leaving only the 6p electron to form bonds, which corresponds to the +1 oxidation state.

### Step 3: Conclusion
- TlCl is more stable than TlCl3, making the first statement false.
- The +1 oxidation state of thallium is indeed more stable than the +3 oxidation state, making the second statement true.

### Summary of Findings
1. **First Statement (TlCl3 is more stable than TlCl)**: False
2. **Second Statement (+1 oxidation state is more stable than +3)**: True